Assuming you are planning a trip from May to September and find a good weather window for the Bimini crossing, that trip is easy in your boat. I've run from Tarpon Springs to the Keys and the Dry Tortugas a couple of times in my 22' Gradys. And back in the days before Loran and GPS, I made a run from Fort Lauderdale to Bimini in a 21' Renkin using a radio direction finder and a compass.
You need to pick your days of course, but much of that trip can be run inside if the seas are rough. The run from Carrabelle to Tarpon Springs is a nice day trip of about 150 miles. Just punch in the numbers for Marker #4 north of Anclote Key. There should be no obstructions on that route since you will be offshore of the rock piles off of Crystal River to Hudson. The next day's destination could be Boca Grande. We usually overnighted at Cabbage Key, which is really cool place.
You can get to the East Coast by taking Okeechobee Waterway from Fort Myers to Stuart if you want to save a lot of time and fuel:
https://www.offshoreblue.com/cruise/okeechobee.php
Alternatively, you spend the night at a marina in Everglades City and head down to Marathon or Islamorada and take the intercoastal to Miami or whatever East Coast port you would like to depart from to Bimini. Crossing the Gulf Stream requires nice weather but it is no big deal if you are properly equipped.