Or would this work, Build the tower in multiple pieces. put cup+ball on top of the uppermost piece, and quickly connect the pieces together in the 2 minute time?
You are not allowed to "modify" your tower after the inital 30 minute building time so this could be a problem. Also the rules state you need to place the cup then it is measured then place the ball. This would indicate it it must be built completely.
I think it would be funny to build something so tall the judges couldn't measure it without knocking it down. They would then need to use a ladder. Since the judges are allowed to place the ball, you could then have them place the ball when they are up there.