Here in Portland, OR, we really only have two seasons: Rain and Cold Rain. I guess Cold Rain starts about this time though.

As a former MUN-er myself, I know that no matter what you try, someone is going to slow it down by either not paying attention or for some inexplicable reason not having access to the voting mechanism. Having a web app would be ideal, since these students (should) all have laptops, but not only did you rule that out, there's always one or two students who don't have a computer. I would just instruct the committee chairs to disallow roll-call votes except on major issues. Voting by raised hands is about as fast as you're going to get under these restrictions, and it's fair to all students.