Well, you may be using the Big CIM motor without an actual gearbox, but the size of the pulleys give you an "effective gear ratio" Much like using a direct drive transmission for your drive train, the size of the wheel makes a dramatic difference in overall speed. Do you know the size of your pulleys in your belt system? Are they all the same size?
I'll make an assumption to give some example numbers. If you use a 2" pulley, the elevator stage will move 3.14" per rotation. So, at 1/2 of the free speed (or at max power) the elevator will be moving at about 5ft per second. [20rps x 3.14"/rotation] That's VERY fast. However, you need to balance that speed with the available torque. Again, at max power (1/2 of stall torque) the motor provides ~18 lbs-in of torque. Since the pulley has a 1" radius, the motor can effectively lift 18lbs, at a rate of 5ft / sec.
A larger pulley provides more speed, but less torque. A smaller pulley does the opposite. As you can see, that Big CIM is a VERY powerful motor to use on an elevator. If you can keep the weight down, you can move it vertically very quickly. We tried to use a couple Globe motors to lift our elevator, but eventually switched them out to use the Big CIM as well. It's a GREAT motor for this application.
I'm interested in seeing some video as well. Although, I can't say I'm looking forward to competiting against them in Hartford!

Another great robot from Team 25. Congrats on another victory!
BEN