I'm not familiar with the ports, but I'm sure it depends on how far you're willing to hop at a time. I also assume there would be some sketchy places, along with some real beauty, along the way. Maybe that's what you're asking.
Yes you can, although don't expect modern marinas all along your trip.
Think more fishing villages if you want to day hop.
Getting out of the gulf will be a climb...current, wind, waves against you.
The coast of Nic has a reputation for being sketchy.
I am somewhat familiar with some of the coast - lived in Panama so know it, lots of info out there on the Rio Dulce, Colon to San Blas and on to Cartagena - not too far, we have an apartment ( family) in Medellin , Cartagena or Santa Marta would be as close as I can get to there with a boat. I just don't know Mexico at all and as pointed out above the coast Nicaragua - zilch - have flown over the area and looked down from the plane - nothing , maybe why they call it Mosquito coast - does not sound too inviting.
Can it be done? Sure, as long as you and your boat are ready for it. Lots of oil rigs in the middle of nowhere, lots of shallow water with shifting sands not quite on your maps, poorly marked channels that lead to local ports, lots of crime (one of minor ones would be stealing everything from your deck at night) and corruption, quite a few places along the way where you will have hard time getting supplies, so plan ahead and keep good stock of everything you might need. Get recent cruising guides for all places you plan to visit. On the bright side: lots of absolutely beautiful places along the way with very few tourists.
Mostly. There really is nowhere to stop on coastal Honduras, Nicaragua and Costa Rica - either for safety reasons, or for navigational reasons. There are offshore islands in these stretches that can be substitutes, like the Bay Islands, Hobbies, San Andres, Providencia, Corn Islands, etc.
Guatemala is relegated to going up the Rio Dulce, which isn't really "port hopping" and puts you in a West hole that can be difficult to climb back out of. Some of the ports are a bit distant from each other, so they won't all be day or overnight hops, but 2- 3 days is probably the max necessary.
I don't have any experience with the area from the Texas border to the Yucatan tip.
if you research your gulf stream currents and flows in gom, as we did, you will find from texas to yukkytan is a nice adverse current named gulf stream. it loops around to south fla and then up east coast. google gulf stream. is enlightening.
you may wish to go east to get west.
head off and around to dry tortugas then across to isla mujeres and then go south. the coast there is sketchy.
check the caribbean cruisers nets for current info, and noonsite--there is one site that presents a lovely graphic showing the current daily danger areas--latest acts of less than friendly nature-- might be a good idea to google it.
you do know venezuela is experiencing some grave difficulties, yes? i would definitely avoid the area as those from usa become incarcerated as spies. there have also been more killings of young citizens by national guard-and burnings of cities and such -- reported by a friend in residence. there is no food or fuel so donot expect provisioning or supplying in vene.
sounds like a most educational trip. should be beautiful.
do the research, however to make sure your adventure is most positive.
i was unable to load your screenshot, but the current is not totally on the nose all the way from tortugas to isla mujeres and it varies a bit on a seasonal basis. we looked at it until we found a positive passage date then we had to cancel due to being called back to san diego by the mooring company for my moored boats. there was minimal effect of potential current againt us when we plotted our course from tortugas to isla mujeres.
as the current loops, there are areas not affected by it wherein we had planned to sail to get from point a to point b, b being mujeres. it seems to be the milk run for that routing. if you notice, there is a broad area unaffected by current as it loops through gom. when we had planned our passage there was only one time we needed to cross that current, not 2 times. we had postponed the trip 2 times to mujeres as the other 2 times we would have had to cross the prevailing current twice. the current showed us different faces each season we looked for our best time to cross.
if you keep a watch on the gom current it is not static. it wanders some.