Continents sliding away from a central explosion does appear to produce the shapes and features of most of Earth's crust in a simple, straightforward way.  Once it is clear that an event happened, the discussion about whether it is possible or not is over, and the question turns to "how?".  How did the landmasses slide?

For perspective, note that while several thousand miles is a long way for us humans, most of the continents slid only 12-16% of the distance around the world at the equator.  Australia went farthest: 23% of Earth's circumference.

People are too small to experiment with huge continents, so any explanation must be speculation.  However, there is an interesting possibility.

An odd phenomenon has been identified on Earth and other members of the solar system.  Large landslides don't just fall to the base of the mountain the way small ones do; they often go great distances, some up to 30 times the distance they fell.

Dr. H. J. Melosh has proposed that long-runnout landslides, earthquake slip, and the making of complex craters reveal a characteristic of the crust.  Put simply, it temporarily acts like a fluid when enough stress is applied.

Well known on a small scale as a Bingham Fluid, Melosh suggests that fluidization at the base of large landslides reduces friction to near zero.  He calls it acoustic fluidization.
Collins, Gareth S., H. Jay Melosh. 2003. Acoustic Fluidization and the Extaordinary Mobility of Sturzstroms. Journal of Geophysical Research, Vol. 108, No. B10, 2473 EPM 4, pp. 1-14.
Melosh, H.J. 1989. Impact Cratering: A Geologic Process. Oxford University Press, New York.
Melosh, H. Jay. Dec 10, 1979. Acoustic Fluidization: A New Geologic Process? Journal of Geophysical Research, Vol. 84, No. B13, pp. 7513-7520.

Another scientist made a similar proposal to explain long-runnout landslides.  "The proposed mechanism assumes that the bulk of material rides on a thin layer of highly agitated particles".
Campbell, Charles S. 1989. Self-lubrication for long runnout landslides. The Journal of Geology, Vol. 97, No. 6, pp. 653-665.

Corresponding to the falling side of a mountain that powers a landslide, the explosive power released by the giant meteorite on impact would have set the landmasses in motion with the force of billions of megatons of TNT, generating acoustic energy.  The continental crust's mass would confine the acoustic energy to the base of the crust.

Shi Jian-chun, Ma Yue-hua, Bao Gang. 2009. The Formation Model of Multi-ring Basins Based on the Theory of Impact Tsunami. Chinese Astronomy and Astrophysics, Vol. 33, pp. 287-292.

There is an important feature of long-runnout landslides that have stopped moving: "Ridges formed at the front and rear of the debris support the hypothesis that the leading edges of the slide initially ground to a halt and the rest of the material piled up behind it."
Campbell, Charles S. 1989. Self-lubrication for long runnout landslides. The Journal of Geology, Vol. 97, No. 6, pp. 653-665.

The Shock Dynamics scenario

In this side view (not to scale), continental crust (brown) is on
basaltic crust and lithosphere (ochre) above the mantle (red).

The giant meteorite explodes deep inside the continental crust.

The force pushes up low mountains, and the landmass slides away like a ship
on water, fluidizing the contact layer.  Behind the landmass, a surface layer of
oceanic crust is melting and cooling to form the mid-ocean spreading ridge
with transform faults, pulled open by the landmass.

When the leading edge loses enough energy, the contact layer at the leading edge
solidifies.  The momentum of the landmass carries it forward like a car hitting a wall,
piling up high mountains.  The formerly fluidized contact layer in front (gray line) is a
Benioff zone, called subduction zones in Plate Tectonics.

With all the action at the surface, it follows that features in the oceanic crust are fairly shallow.  They include these:

Mid-ocean ridges and transform faults, where surface melting results from the removal of the weight of continental crust (pressure relief melting).

Trenches (green line) along the leading edges of landmasses result from the rapid application of the weight of continental crust.  Towards the end of a continent's run, friction compresses the leading edge, raising mountains.

A crustal wave (red line) from the low angle impact was launched in the direction of travel of the meteorite, and "froze" in the end to form an inclined trench.

 
Wave diffraction

How the Shock Dynamics event left the
appearance of Plate Tectonics

The boundaries of the "plates" (spreading ridges and subduction zones) formed during the Shock Dynamics event, except for the East Pacific Rise which formed much earlier following Earth's grazing collision with a planetesimal that produced the protocontinent.  That "subduction zones" are as described above and not sinking slabs is evident from the fact that "large, intermediate-depth (60-300 km) earthquakes have subhorizontal rupture planes."³  That is, earthquake faults at these depths are close to horizontal rather than at the angle of the supposedly diving slab.

Once the sliding landmasses slowed sufficiently, the lubricating mechanism beneath them was lost and the continents became firmly attached to the lithosphere.

Plates

Oceanic lithosphere is roughly 100 km thick.  Plate Tectonics theory is based on the notion that the lithosphere is formed at mid-ocean ridges and dives into the earth at trenches.  This is not the case in the Shock Dynamics theory, which says that the divisions in the lithosphere are features that formed at the surface and extend deep into the lithosphere, enhanced by "slow motion" differential rotation (see below).

There are substantial areas on the Earth that are not part of the 14 large "plates" of Plate Tectonics theory that one hears so much about.  A study has found 38 additional "small plates" plus a number of zones designated as "orogens" with fuzzy plate boundaries.  The largest "orogen" stretches from Korea to the Alps.  Another covers Alaska and its connection with Canada.  Most of the small plates (or microplates) are in the region where the Australia-Southeast Asia block shattered against Asia and scattered to the east.  These exceptions to the rule require special interpretation in Plate Tectonics theory, and bring to mind the attempts to salvage the Earth-centered view of the solar system by adding "epicycles" to the orbits of planets in the days before Galileo.
Bird, Peter. 14 March 2003. An updated digital model of plate boundaries. Geochemistry Geophysics Geosystems (G3), Vol. 4, No. 3, 52 pages.

"In the classical view, the motion of a plate was driven from within by body forces".  "However, a common hypothesis is that microplates are externally driven, i.e., that larger neighbor plates determine their motion."  A study of the Baja California microplate indicates that it is loosely coupled to North America, and that 90% of its motion is from being dragged by the Pacific plate.
Plattner, C., R. Malservisi, R. Govers. April 2009. On the plate boundary forces that drive and resist Baja California motion. Geology, Vol. 37, No. 4, pp. 359-362.

In the Shock Dynamics view, this kind of jostling is what is occurring today all over the globe on every "plate" in slow motion.  "Large plates move coherently, being decoupled at the Low Velocity Zone (LVZ).  They show that the force acting on them is uniformly distributed and not concentrated on their margins."⁴  In fact, the principal driving force of Plate Tectonics theory, slab pull on a plate margin, "would be stronger than the strength plates can sustain under extension (pull)."⁴

Slow Motion

If the work attributed to Plate Tectonics over 200 million years was actually accomplished by the Shock Dynamics event in 26 hours, what causes the few centimeters per year of motion of the "plates" measured by GPS?

"The fact that plate velocity on Earth does not depend on plate size and that the velocities of the fast plates do not depend on length of the subduction boundary suggests that it is the system, not the individual plate, that dictates plate motions."  "The possibility that has been overlooked is that the plates define and organize themselves by mutual interactions of the whole plate system and that minimization of dissipation in the lithosphere may be the organizing rule."¹

A number of researchers^4,5,6,7 have picked up on the fact that the lithosphere constantly drifts slightly to the west relative to the mantle below it.

"In the hotspot reference frame a 'westward' rotation of the lithosphere can be observed.  The origin of this net rotation of the lithosphere is still under debate, but it should range between 4.9 cm/yr and 13.4 cm/yr at its equator."²  In the differential rotation model, the lithosphere and outer core show a net westward drift, while the mantle and inner core move eastwards.¹

"Because the Antarctic plate is centered on the Earth's south pole and is nearly surrounded by ocean ridges, it can be regarded as an inertial reference with regard to Earth's rotation axis."⁵  Where the crust is thickest, such as under mountain ranges, there is the most contact with the eastward moving mantle.⁵

Proponents of differential rotation find that the axis of rotation of the lithosphere relative to the mantle is different than the rotational axis of the whole Earth:

Global lithospheric net rotation relative to the mantle assuming a
mid-asthenospheric source of the Pacific plumes.²

Transferring the rotational path in the above illustration to a globe yields the red ring below.  For reference, the blue ring follows the equator.  The orange button at the top marks true north; the purple button marks present-day magnetic north; and the red pegs mark the axis of the red ring.

The rotational path above (red band) "has an angle of about 30 degrees with respect to the equator, close to the revolution plane of the Moon about the Earth (28 degrees), although this overlap is intermittent."⁴  This is significant, because tidal force provides a constant westward pull on the lithosphere.

The approximately "2 - 3 degree tidal lag angle between the tidal bulge and the gravitational alignment between the Earth and Moon determines a permanent torque toward the "west", opposite to the eastward rotation of the planet.  This torque is considered responsible for the secular deceleration of the Earth, and acts directly on the lithosphere."  "To conserve the angular momentum of the system, the Earth's deceleration is mostly compensated by the enlarging of the Moon's orbit, at a rate of 38.2 + 0.7 mm/yr."⁴

"The solid Earth tides have a well-known vertical oscillation of 300 - 400 mm/12 h 25', but they also have a relevant 150 - 200 mm/12 h 25' horizontal swinging [i.e. stress loading].  Under a permanent torque, this oscillation may induce a tiny strain in the upper asthenosphere, say 0.1 -0.2 mm.  The cumulative effect of this small horizontal motion... may well reach several centimeters (7 - 14) per year".  "The advantage of this mechanism is to act contemporaneously all over the lithosphere."⁴

"The idea of tidal drag as the driving mechanism for plate tectonics is particularly intriguing because it is energetically feasible.  In fact, the dissipation of energy by tidal friction is slightly larger (1.6 x 10¹⁹ J/yr) than the energy released by tectonic activity (1.3 x 10¹⁹ J/yr)."⁵

When differential rotation was proposed as a driving mechanism in the early years of Plate Tectonics theory, opponents "discarded Earth's rotation as the cause of the westward drift, claiming that the viscosity necessary to allow decoupling between lithosphere and mantle... is too low when compared with present-day estimates of the asthenosphere viscosity."  "Tidal torque provides a sufficiently energetic mechanism to drive this motion, but requires a mechanical decoupling between the lithosphere and the deeper mantle that is incompatible with current understanding of upper-mantle viscosity."  However, "the mantle very likely has a nonlinear rheology, and the viscosity of the asthenosphere can be far lower in thin, undetected layers."  "A thin, low-viscosity layer (shear zone) could accommodate this motion."⁵

The lower picture is a cross-section of the Earth along the red line in the upper picture.  The black dots in the upper picture are stations from which seismic readings were taken.  The lower image is called an "absolute shear wave velocity model".  It shows "a pronounced global Low Velocity Zone (LVZ) at the top of the asthenosphere, which is strongest underneath the oceans, but is also clearly identifiable underneath the continents.  This level is here inferred as the main decoupling zone at the base of the lithosphere, possibly having an internal sub-layer with ultra-low viscosity, much lower than the average asthenosphere."⁴

"The viscosity in... the LVZ of the asthenosphere can be much lower than present-day estimates of asthenosphere viscosity based on post-glacial rebound, because horizontal viscosity under shear can be several orders of magnitude lower than the vertical viscosity computed by averaging the whole asthenosphere."⁴

There is some evidence in two studies of North America to suggest that there is an ultra-low velocity zone at the top of the LVZ, due to shear stress lowering the viscosity of the upper asthenosphere, using the standard assumption of non-linear rheology of the mantle.⁴

In the Shock Dynamics view, the "frozen" edges of crustal waves in the Pacific and beneath the leading edges of continents that moved became what Plate Tectonics calls plate boundaries.  They are zones of weakness in the lithosphere, subject to shear, compression or extension.  These angled faults solve the problem of subduction initiation that plagues Plate Tectonics.  Known as Benioff zones, they vary in depth up to 300 km, and apparently engage the upper mantle in its relative eastward motion, as do other deep sections of the lithosphere.  Thus the tiny measured motions of the "plates" is the interaction of regions of the lithosphere with the mantle as the lithosphere drifts westward due to tidal forces.

1. Anderson, Don L. 2002. Plate Tectonics as a Far- From- Equilibrium Self-Organized System. in Plate Boundary Zones, Geodynamics Series 30, American Geophysical Union, pp. 411-425.

2. Doglioni, Carlo, Eugenio Carminati, Marco Cuffaro, Davide Scrocca. 2007. Subduction kinematics and dynamic constraints. Earth-Science Reviews, Vol. 83, pp. 125-175.

3. Kiser, E., M. Ishii, C.H. Langmuir, P.M. Shearer, H. Hirose. 2011. Insights into the mechanism of intermediate-depth earthquakes from source properties as imaged by back projection of multiple seismic phases. Journal of Geophysical Research, Vol. 116, B06310, pp. 1-26.

4. Riguzzi, Federica, Giuliano Panza, Peter Varga, Carlo Doglioni. 2010. Can Earth's rotation and tidal despinning drive plate tectonics? Tectonophysics, Vol. 484, pp. 60-73.

5. Scoppola, B., D. Boccaletti, M. Bevis, E. Carminati, C. Doglioni. January/February 2006. The westward drift of the lithosphere: A rotational drag? GSA Bulletin, Vol. 118, No. 1/2, pp. 199-209.

6. Smith, Alan D., Charles Lewis. 1999. Differential rotation of lithosphere and mantle and the driving forces of plate tectonics. Geodynamics, Vol. 28, pp. 97-116.

7. Smith, Alan D., Charles Lewis. 1999. The planet beyond the plume hypothesis. Earth-Science Reviews, Vol. 48, pp. 135-182.