We used 12:1 banebots transmissions directly driving 8" AM mecanums in our Rack'n'Roll robot. It worked pretty well
http://www.youtube.com/dtengineering#p/u/12/gyn9e0cT3-A and we were able to make it up a 30 degree incline.
The banebots trannies needed the long output shaft that is currently backordered, as are the BB P80 transmissions.
An AM toughbox with the long output shaft for each wheel should work well, too... although I'd highly recommend getting the aluminum gears to lighten it up, and maybe even speedholing them a bit. Four transmissions and ten pounds of wheels can start to add up quickly.
Jason