I am going to try the binder clips. However, I had another idea that I might try.
On the backside of the boards, glue some thin refrigerator magnets. Then just find a few flat strips of metal that can be magnetized, and slap the board down on those suckers, line it up, done. Of course, if you don’t want to permanently modify your boards, then this wouldn’t be for you.
If I end up doing it, I’ll let you know how it goes.