[Chris is me]

There's a reason most drivetrains have six (or more) wheels in them. Given the pre-2013 robot dimensions, in the long orientation, four wheels at the corners just will not turn very well. This is occasionally a desired feature (see: a butterfly drive), but you need SOME way to turn.

One way to do this is to use different traction materials on each wheel. The problem is that by compromising traction on half of your drive, you are losing out on pushing power to an extent as well as pushing resistance.

Another way turning is accomplished with 4 wheels is to shorten the wheelbase such that the four wheels are closer together. To maintain stability, you have to add casters or unpowered omni wheels that will hold your robot frame off of the ground, as your wheels are now much closer together. However, unpowered wheels rob normal force from your powered wheels, which results in less pushing power.

Going to six wheels, with the center wheel "dropped", effectively halves your wheelbase length, to the point where the wheel base is notably wider than it is long. Depending on the drop, wheel material, etc. you either ride on four wheels at a time, or all six wheels touch the ground due to tread compression. In either case the middle wheel takes most of the load and turning about your robot's center is easy.

The tricky thing is that a six wheel drive can't all be direct driven out of transmissions like you want to. If you must avoid chain or belt at all costs, and you have access to precision manufacturing of some sort, you can do a gear drive, similar to what 829 did this year. With aluminium gears readily available, it's not as much of a weight penalty as it used to be, and it does prevent any chain or belt issues from popping up. That said, using 35 chain is honestly not that hard.