I used to have problems with this too. My problem seemed to be that I was using too much glue and it was ending up running down the paper and sticking all over the frame.
Now, when I can I just "stick" the frame together over the plans with just enough thin ca to hold everything together, and remove it from the paper, then go back and reinforce all the joints while holding the work, this way you can hold at any angle necessary to end up with the glue where you want it instead of it all running straight down.
Be carefull, now that your work is not attached to the nice straight building board, any lumber which was warped to begin with will want to go back to its origonal shape, youll need to set it back on the plan after removing it and be sure everythings still flat and straight, keep this in mind and youll be OK.
I find it easier to do it this way than to remove thick ca ect. from balsa.