Advice for The Infinite (Act 3)

I'm having trouble progressing to the final part of Mewgenics.

I have: A small breeding pool of 7x7 cats with 10 mutations (often random)

A fight club

A pool of inperfect stats cats

I used to have a shitton of kitties, but since I started farming for rare furniture and so on, the numbers for all my cats have been severely reduced. My imperfect cats oft die in Act 2 by the robots, though sometimes I am able to get the rare furniture, or even as far as to defeat Hitler.

My perfect cats have been able to clear all the way to The End, but I haven't been able to progress further.

Would appreciate any advice.