I dont know about the shuttles, but for another option, you can also rent from
Alamo at the Dolphin resort. I just booked a car for 1 day (actually 13 hours), today through them. They did note that they close at 4:00pm, however they will give us instructions how to drop the car off after hours.

At any rate, you can either take busses or walk (depending where you are staying) from the Dolphin, so there's no need to worry about a shuttle.