Same issue here with the minimum number of days requirement. We've been using National our past few trips and they've been generally great to deal with. Sometimes they'll let us leave the car and keys with the charter company when we leave, other times they want you to bring it back and then they'll take you back where you need to be. On the plus side, they're at east end, RT and west end, so pretty much wherever you are, there's an office pretty close by.

Haven't done AVIS, but I'd bet if you check you'll find they're similar. If not, check out National, which I think is same as Budget on Tortola.

Would be happy to support the local guys, but the minimum days of rental just rarely works for us.