Your estimate of the gravitational potential energy available is way too high.

The potential energy of a falling body is calculated by integrating the force across the distance. But the force is not constant as the altitude increases, it decreases as the inverse square of the product of mass and acceleration. The gravitational acceleration is not the same at geostationary orbit altitudes as it is at the earth's surface.

Near the surface, (say, when you drop a rock off a building) you can assume for simplicity of calculation that the gravitational acceleration is the same at the top of the building as it is at the bottom. For all practical purposes, they are almost identical, but not quite. Over long distances, you cannot simply subtract the two radii and use the diifference to give head.