Perhaps take it room by room and block access for your cat while working?
That's the sort of thing I'm thinking, it just feels like one of those puzzles with the sliding squares. Not least because while we're trashing our bedroom we need somewhere to sleep and while we're trashing the workshop/office we still need to be able to work.
Something tells me I'm going to be testing the limits of the guest bedroom...
Blocking access for the cat is often easier said than done. He just wants to be where we are, and it only takes opening a door a crack and he leaps through. We are going to have to teach him a new location for a secondary food and water bowl and a secondary litter box, because I want to do some major work right next to where his current food and litter box are.