[pfreivald]

I highly recommend direct-driving mecanum wheels off of Toughboxes or Planetary Gearboxes (like Banebots P80s). Any gear ratio from 9:1 (probably too fast for this game) to 14:1 (perhaps just a tad too slow) should work well.

Support the shaft on the other side of the wheel (which will protect it from impacts, too.)

That's about as foolproof a mecanum setup as you're going to get, and while it might not work straight out of the AndyMark box, it's something you can whip up with some aluminum from the local hardware store without too much effort.