Amazing how great minds think alike!
What you describe is almost exactly what 1213 did for '05.
Cad here:
RealDeal Here:
We did not use chains. Direct drive with a 4 inch wheel produced a zippy 7-1/2 FPS The drive platforms have 60+ matches on them and mucho hours of practice without a single malfunction - other than a drive shaft snapped in practice right where it's machined down from 1/2" to the 0.3 x 0.25 double-D to mate with the tranny output. That was solved way before the first competition by heat treating them.
You're right about the turning issue. We solved that by moving the front wheels 5" back to shorten the wheel base, and by using 95A durometer wheels. Wheelie bars 1/4" off the floor at the corners kept it from tipping.
The design worked just fine for Triple Play. OTOH, it would never work for a game like Stack Attack - with the ramp and all that pushing.