Not trying to bump my post so quickly... I just worked a bit more on it, and have another pic to help show what I'm trying to do a bit better. In this pic, I need to roll the white part around the red cylinder 1/4 of the way. I drew some of this in my model and tried to find some commands for it, but still have nothing.
If there are no special tools for this, I can just measure 1/4th of the circumference and cut out that much of the white area, and then revolve the remaining white material to where it would end up and do something to fill in the actual radius part of the white. That's how I'm going to proceed for now.