600 is a lot of cats Brian.
You have it working. But would be great to figure out how to run with less labor.
Wondering about Michaels method of leaving a thin skin. Would not require a vacuum, just make it a little thicker. (absolute vacuum can only get ~15 psi, so fundamentally limited but maybe leave enough to support the entire set at once). Then flipping the entire panel and running through a drum sander to bring them down and remove the skin all at once. Which also produces a sanded part. (as long as they stayed down.... cats make me nervous, dogs would be inclined to behave better)
(a quick search found a post where they left a thin skin then flipped, finished sanded with a hand sander and the parts fell out...)