I left the cats as an optional thing, because it would get very tedious it you had to find all of them. But as a personal challenge, I think it works.
I had some playthroughs where I got to the exit safely, but went back for more cats, and ended up failing as a result. So it has an interesting balance of incentives ... something I never really planned for, but due to the fast decision making that had to be done, I think it works better than anticipated.