According to an internet web crawl I'm the only human being on Earth who can't figure out stage 24, which looks like an exercise in brute force because there is no coherent problem solving mechanism applicable just try your 5 pieces in 6 slots until one presumably works.
For anyone struggling on the 3rd ending (as in, ending 1), the trick you need to figure out is before you choose paths. Being more precise would only cheapen the experience so I won't.
The secret of level 17 is to not open every key and press the most recently available switch at the first opportunity. You need to strategically not hit things.
The punching instead of running thing needs fixing, but at this point a nerf isn't what's called for. I would buff walking to be at least equal in terms of distance per stamina.
For 1-11, every time you respawn you get a cat on ALL activated flags plus one other. If you activate flags with two cats at once then die without touching other flags you can get more cats. Also you can push dead cats through spikes and if they hit a flag they come back to life. Before you get the rescue on that stage you should start a life with 4 cats total.
If coming up with ways to make a sequel, may I suggest knock-out blocks? If you have some number of times per stage you can destroy a block and you have to decide when to use it when unfolding a piece that could add a much needed tactical element. Or some blocks that you don't need to fill and if you unfold something into it creates a hole there. The current stages have a lot of symmetry and that puts an effective cap on the potential difficulty.
I was also suck for days when that level was in design stage.