The entire State of Florida is typically considered a single location for one-way rentals, there are no one-way fees between locations. Rentals in Florida are also typically much less expensive than in the NYC metropolitan area. Because of this I would suggest you pick up your car in Florida as soon as possible, in your case, it sounds like the Jacksonville Airport would allow you to trade out your one-way rental for the Florida rental.

Also, it's almost always a bad idea to buy gas from the agency. They will charge you taxes on top of the fees they quote plus you're not going to be able to get the tank completely empty plus the tank most likely will not be completely full when you pick up the vehicle, in effect making the per gallon rate even higher.