I have no experience in Florida other than a vacation, so please ignore if this isn't of interest.
I was able to set up my trust through the dealer who sold me my first suppressor for ZERO ADDITIONAL change. It was a serve they offered to allow people to protect themselves in this state (Washington). You might want to check with a couple of Class III dealers in your area and see if they offer the same service.
My trust was a matter of 7 or 8 pages of paperwork and they filed it for me as part of the application with the ATF/Feds on the purchase of my suppressor.
Good luck. Definitely go with the trust as you can then "bequeath" the suppressor upon your demise to a family member or friend who can pass the background check and pay the $200 transfer fee.