I live in MN, so I'm sorry if this doesn't apply, but I got my name changed a month before starting T. My current name, Chris, is a heck better than my old, feminine, "it's so pretty, why would you ever want to change it" name. Trust me, I feel you.
What I did was apply for a fee waiver. I am not on government assistance, but I make little and qualify someone living in poverty. Just be honest and tell them how much you make, any assistance you are on and how much you get, and fill it all out along with your name change documents. You'll get notified via mail if you were approved or denied, and it takes 1-2wks to know and 4wks until your court date, where you need two people as witnesses. I only had to pay for my fingerprints and such, but its cheaper than almost $400 for a name change!
Again, this is in MN and I don't know how it might differ from FL. But it might work. Good luck!