Uber to the west side of the airport and you'll save $150 in taxes and fees in exchange for a 10-15 minute ride. Should be no more than $15.

Alternatively, split the rental period so you are taking the airport's car for only a day or two. Since there are no drop fees in Florida you can one way from the airport to X6M or whatever else is convenient and one way from there to Tampa. Unless the car is almost due for service they'll let you keep the same car if you ask.

The split rental will cut down the savings a bit, but will be a lot more convenient if you aren't traveling alone.