I never did a top with Plexi since it probably would warp with any heat source (lights) placed above it. I think having a nice piece of glass cout would be better... as your finding out.
As for doing the doors with the plexi-glass, I use magnetic strips along the edges to keep it pulled in tight and not warp. The strip come in a roll for about 6 bucks and can be cut with scissors.
Oh i see, your just doing the doors. Interesting that the magnets keep it from warping. I may consider trying to make a door out of plexi glass then. Haha yeah i learned my lesson for the lid about a year ago. No more plexi glass lids!