[GeeTwo]

It's wonderful to see that someone's going after this idea! Given that bevel gears are essential to this working, my thoughts on this line were to go OTS on this, using something similar to one of AndyMark's LJ bevel boxes (am-2796 or am-2622), each of which already include a 2:1 reduction. I'd love to see my vision of a "dizzybot" become reality using something like this. The "dizzybot" would have the full capability of a "unicorn swerve" that is software-constrained to prevent slipping wheels, but with only three control pins needed from the 'RIO:
Control #1 - steer all the wheels relative to the base frame (all of them always point the same direction)
Control #2 - spin the wheels against the floor (all at the same speed, always)
Control #3 - spin the superstructure relative to the base frame (since the base frame ideally never rotates)

The simplest implementation I can imagine would be to put all of the electrical system on the "superstructure", and extend three shafts and sprockets (or gears) down to the base structure.