If you're sure you're quitting, I'd consider going ahead and using the floaters as soon as possible because I can see your boss escorting you from the building the instant you give notice, and then refusing to pay you for the floaters since you weren't at work. It would be inappropriate for your boss to do that, but I think it's clear that "appropriate" isn't really on your boss's radar screen.
Congrats on getting out of that environment.
I had a roughly similiar situation happen to me years ago. We had PTO and I was going to take a 3 week vacation overseas. In January, I emailed my boss and requested the specific dates for August/September. He replied and approved. DH and I booked the hotels, the airfare, the rental car, etc.
In July, that boss was laid off and I got a new "temporary manager." In August, I mentioned to her that I'd be gone at the end of August for 3 weeks and she laid into me that it was unprofessional that I was going to take a last minute
vacation and didn't get approval or tell anyone, etc. She was awful to work for for many other reasons as well.
I had saved all the emails from the previous boss approving my time off. It wasn't my fault that the company did a lousy job of communicating and listing vacation dates. I forwarded the emails to her so she begrudgingly let me go on the trip.
But the whole time I was gone, I was planning my exit strategy. I couldn't stand my new boss or the company. I stuck it out for 6 more months until I had a new job offer and I quit this old job.
I'm glad you're in a position where you can tell them to get lost. I look forward to the update!