My simplest thought is to use 1/2" plywood for the door and make your wooden track-groove 3/4"-1". Leave lots of slop for the door to slide around in. But I don't know how critter-tight you need to be for any predators.
Discussion
If your opening was a 1' square, maybe make the door a 14" square and use a 1×4 screwed vertically on both sides with a 1/2"-3/4" gap. Then screw a 1×6 to the 1×4 so it overhangs to form the outer edge of the track. If you made those 30" tall, you would be unlikely to pull the door out of the track in the up position
My biggest concern with critters is possum and raccoons. I’ve heard stories of raccoons even lifting automatic doors and getting into coops at night