Thanks for the feedback everyone. We ended up adding a second set of high-traction wheels in place of the medium traction wheels, and leaving the omnis in place (which don't have any drive power). I was a bit suprised to see us turning so nicely with all that traction, but it seems like we're going to stick with this setup (plus it took more than 2 hours two change out the wheels, so nobody really wants to experiment anymore

)