Hey, individual small prints on sticky paper is a good idea. I had a little bit of trouble getting everything to line up properly across my single 53"-wide print.
I think a little thin layer of rubber cement or something similar would be all you need to hold your artwork down, since it will be under plexi. A lot of the artwork might not need anything sticky at all, since there will be buttons poking through holes in it, keeping it firmly in place. Between the plexi and buttons, you probably wouldn't be able to move most of the pieces around even if you tried.