Great post, welcome!
I think your basic plan is terrific. I do not have your experience on a boat, but I am experienced at travel, and I can tell you that you'll have an easier time outside the United States than in it if you just want to move from place to place and make your way. Inside the United States everyone drives their own car so hitch hiking and things of that nature are frowned upon these days, but outside the U.S. especially in places like Central America that's just how you get around, very few people own their own vehicles, that is a luxury, so getting from place to place is a lot easier without your own car. You can also pitch a tent just about anywhere and all the rest.
Your basic strategy of making your way around on different boats is, I think, very sound. I would think that there would be some important places where you would be more likely to catch a boat and that you would essentially be moving from one hot spot to the next while at the same time enjoying the world around you and taking side trips along the way. I do not have first hand knowledge of these places, but the two entrances to the Panama canal would be an obvious example. I know that hitch hikers do much the same thing, they don't want to be dropped off in the middle of nowhere on some rural dirt road, they want to be dropped off either near a major highway or at a truck stop if they can, or at least at a popular crossroads, because that is where they are most likely to get a ride to their next destination. I bet if you were in a place like Panama you could help people move their boats through the canal until you find a boat that is heading your way, for example, it would give you the chance to prove your usefulness as crew, I understand the boats actually need your help negotiating their way through the canal. Other big destinations like that would probably be the areas in Florida where people hop off to the Bahamas, any island port, and anywhere along the milk run especially places like Papeete where a lot of long distances cruisers stop over for supplies and repairs (and probably lose crew who are sick of the ride). I'm sure there are lots of other places that you already have in mind, you probably know more about it than I do.
Having done a fair amount of travel I can tell you that you won't regret it, there is nothing like going out to see the world to make life fresh again. I have done some trips that are similar to what you are trying to do where I knew where I was going, but I didn't really know exactly how I was going to get there, but I went anyway. Those were some of my favorite trips too because half the fun is the adventure of it all. I would, of course, always recommend you have a way out in an emergency, just in case, because you don't want to end up stranded somewhere and have no way home.
The only disadvantage to your plan is that you might not get to see all of the sights that you want to see unless you are prepared to rough it. Not having your own transportation you'll be forced to catch rides and take public transportation, and in urban areas that isn't so bad because you always have youth hostels to fall back on, but out in rural areas like where many of the Mayan ruins are you could face some challenges. In some parts of the world you can't even really travel without transportation because it is too hot, too cold, too dry, and just too much trouble to do it. Some places are also just dangerous for solo travelers, especially near tourist attractions and in urban areas, and I have always tried to avoid those areas when I was traveling alone.
We all look forward to hearing about your progress, sounds like a lot of fun.
Best of luck.
Edit - I wish I had your experience.