Oh, if you haven’t got flights already (but it sounds like you have) have a fiddle with the BA customised trip tool.
It can throw up some bargains when you mix and match flights with hotel and/or car.
Note: not the regular flight + car booking option, find the customise trip tool.
Car hire prices are ridiculous all across the States throughout this year.
I’d suggest trying any of these to see if they can give you a better price (they all do car only):
Virgin Holidays
British Airways
Autoeurope.com
Hotwire.com
https://www.discountfloridacarhire.co.uk
With the latter...