Calculating surface fragments (continents) on an expanding sphere (Earth)

Let's suppose plate tectonics is wrong and our planet Earth has expanded over time, the continents being the remnants of a crust that once covered the entire surface of a smaller planet, the oceans floors being extruded mantle, a manifestation of expansion.

http://earthexpansion.blogspot.com/2011/02/earth-expansion-synoptic-simplicity.html

http://earthexpansion.blogspot.com/2011/02/synoptic-simplicity-again.html

It is difficult to visualize how everything would have looked like on a smaller Earth. Well, some people have made visualizations, but what about calculations?

Unfortunately, my experience is exclusively in Boring Business Brogramming. So when thinking about whether a development such as the Americas swiveling open to accommodate the Pacific is possible, I don't even know how to approach this problem.

Given today's Earth and geometrical data - a sphere (kind of), surface fragments (continents, polygons?) - would it be possible to retro-calculate the Earth to a smaller size, considering certain constraints (continents cannot be arbitrarily deformed) in order to find out whether a given movement story for expansion makes sense geometrically?

How would you go about doing it? Concepts, approaches? Tools, techniques? Sources for geo data?

Update

An important factor to take into account in reverse engineering the Earth to a former continental configuration on a smaller planet is the age of the ocean floors as measured by the U.S. Navy and others. As you can see on the map, the ocean floor is very young everywhere as compared to the continental crust. Moving back in time and deflating the planet, the youngest ocean floor stretches (red, at the spreading ridges) will have to be removed first because we know they weren't there.

So these measurements significantly constrain the problem of surface reconfiguration on a shrinking sphere. Still, I'm clueless as to the geometry to use in such a problem.

From how I understand your problem, the surface areas of all today's continents would be the same in any given time, while the total surface area of Earth would shrink as you move back in time. Right?

So the question is whether the continents can be placed on the Earth so that their total surface area does not exceed the total surface area of Earth for that moment in time. And there are some constraints to this problem: you cannot make the continents jump from one hemisphere to the other in a short period of time, for example. So you'd have to take the incremental movement of continents into account.

Tricky one. The closest problem that's related to this is probably Algorithm for fitting 2D polygons in an area? But the additional possibilities (like breaking a continent into several pieces, if that's allowed by that theory) makes it a pretty hard one.