Interesting... I'll have to follow this.

Just a few observations etc...

I'm assuming the rate of continental drift slows as the continents near the edge due to the greater area for them as opposed to the centre where everything is crammed together?
Do the continents kind of cling to the edge before sliding over?

I'm also curious as to what you meant by a few thousand years... Long enough for great empires to be established in regions of Mediterranean climate and for them to build great cities to stand the test of time, only for it to fall as the climate gets too cold for them to adjust, leading to their cities to be abandoned in a frozen wasteland for thousands of years waiting for intrepid adventurers to attempt to steal the fabled treasures lying in the crypts beneath the great temple?
Or short enough that no sane person builds anything well enough to stand for two thousand years because they'll be packing up and moving closer to the centre long before it falls down?
In short... How many thousands of years are we talking about?

Also, is there anything on the other side? Has anyone bothered to go and look? Obviously a journey of epic proportions that would make Journey to the Centre of the Earth look like a picnic in the park in comparison.)