One item to be aware of is Unistable Polyhedra. The surface area on the projected sphere doesn't matter much if a face happens to be unstable.

Also, the surface the object is tossed at matters ... pitch, felt and glass can cause a die to roll differently. In experiments with 7-sided pentagonal prisms, put through thousands of rolls... a pentagonal prism could be made fair on one surface, but not be fair on another surface.

When I looked at the problem, I built up markov chains on how faces toppled to other faces based on toppling angles.