I would actually recommend one of the bane bots motors along with one of their planetary gearboxes if your team has the ability to press the pinion onto the shaft.
Either the window motor or the fisher price motor is likely to be the easiest to work with. Remember if you are pulling a cable, with some pulleys your motor does not have to be at the end of your arm. Also use a limit switch to keep your motor from letting out too much string or cable and causing a backlash.
The reason I do not recommend a servo in the application you plan is the very little torque that it provides. Yes the continuous rotation one can be geared down using parts from
www.servocity.com however you will likely spend most of the match waiting for it to close on your tube tightly enough to hold firm.
This could be a good use of a small pneumatic cylinder as well.