I think
Team 25's solution was pretty elegant: they clamped the motor with a plate on the back (commutator) end which pressed the motor axially against their gearbox. A pin in the gearbox face located the end of motor to prevent rotation under torque reaction. I think they milled a shallow bore in the gearbox faceplate which was a slip fit on the end of the motor to locate the output shaft center.
Their setup allows rapid motor changes - just remove the two screws holding the back plate to release it - and the aluminum gearbox faceplate conducts some heat away. Plus the entire motor body is exposed for air cooling.
Can't say I'm a big fan of Lexan (aka polycarbonate) for applications like this. It may be very tough, but it isn't very dimensionally stable and it doesn't conduct heat well, either.