I have done that with DeDe's a few times but I believe I read on here that Deadman stopped doing that. I sure hope not because it was GREAT!!! We would get in late at night and the car would be waiting with keys under the mat and we could use it to provision and such and then just leave it in the parking lot with the key under the mat. His email address is
dedescarrental@surfbvi.com If he is doing it I'm sure he wouldn't care where you pick it up at. We did the same thing in reverse from the airport (much like you want) and had a car waiting at the end of the charter and used it that day and dropped it at the airport the next day.