I cheated and looked at the comments, I hadn't thought about switching patches as a mechanism for getting through the game. That's really funny, a real creative twist!
Viewing post in Do NOT pre-order games jam comments
*spoilers below*
Hmmm, sword should've been working in the invisible mode too, I just ensured: https://imgur.com/a/UQOfukW. Was you able to swing with it but it didn't kill the boss or you couldn't swing at all?