Gas or Diesel? I will guess it's a gasser, not that it matters just wondering about your cruising speed and consumption. For example, we travel from the Ft. Myers area to Elbow Cay in the Bahamas every year. It's about 400 miles. We get about 1.5 nmpg. We stop in Clewiston, Stuart, North Palm Beach, West End, Spanish Cay and then White Sound. Invariably we get stuck at Stuart waiting on a window to cross the Gulf Stream. Logistics make it convenient to stop and wait there instead of North Palm.
So, we blew about 100 bucks in Clewiston, then 600 in Stuart for a month and put 350 bucks in diesel into the tanks. Then a night at North Palm and West End, which is another 200. Fuel at West End again, maybe 400 bucks. Spanish Cay adds in about 100 as well. So adding that up, it takes about 1400-1500 bucks to move the boat over here. Considering that the montly stay is a constant no matter where you are, one could argue that should not be included. You will pay that along the way waiting on a weather window, or, at the home port after arrival.
Looking at the itinerary, quite a bit of this is on the river coming South.
Hopefully by the time you reach the GOM you have a good handle on the boat. Certainly before leaving you have picked up spares that include filters, plugs if required, caps, rotors, impellers, belts and such. You might even change the oil before leaving unless it is CLEAN.
Once down on the GOM, look over all of the alternative ports of call.
But more importantly, get some online charts and software. Load up and plan the journey. You may be pleasantly surprised to see that a large portion if not all of this is possible via the ICW in relatively protected water. For example, get set up on activecaptain.com and then look at the online cruising guide with the nautical chart view. You will see all of the marinas, anchorages etc.. It's a terrific resource.
I say goferit. You'll have a great time while improving your skills and knowledge of the boat. More over, you meet a mess of new folks and probably make a bunch of new friends.