Regarding the car question, I would just contact a couple of car rental guys directly. No one here can tell you what their policies will be, especially on a big holiday like that. Jerry's is a TTOL sponsor, so you could consider using them to thank them for their sponsorship here.

I agree with Mal though, don't stay in Roadtown. Cane Garden would be a much better choice, or Seb's, although I'm wondering whether it's a bit late to get reservations. There may not be much available at this late date!