To the extent of my knowledge, there is no public range in Central Florida that will allow you to do what you want to do. For obvious liability reasons, public ranges are not allowing randoms off the street to pay $20 and set up a 32 round field course. Unless you have access to private land, you are going to need to join a club. Even with some of the member only ranges, there are restrictions. I would check the rules at WAC and Guncraft as they are more convenient to you in Tampa. Universal is a great facility, not sure of their member rules either.
Volusia County Gun and Hunt Club is great but a bit far from you. They allow what you are seeking. However, I believe last shots are at 5pm or so. They have ROs on property at all times. This is the deal breaker for me as it eliminates the possibility of shooting after work
CFRPC (I am a member) allows holster work, steel etc. on the action range after you have become a member and then taken a secondary qualification. Slightly annoying bur totally worth it. Range is open sunrise to sunset. Only issue here is that you have to get creative if you want to build a mini practice stage. The only thing that they provide are target sticks