I am at a Crossroads

What about the possibility of storing it somewhere in the US? Too expensive? I know a place in Charlotte, NC that sells collectible cars but also keeps cars in storage for local owners, esp. in winter. I have seen cars sitting there indoors, batteries on a trickle charger. Perhaps with the money you save by moving south something like that might be an option. Fly in every once in a while and drive it around. Then when you are settled down south just ship it (to the US-Mexico border?) or drive it. I know. It’s easy for someone else with no financial stake to make such a suggestion.
One other thought. Titling and plating a car “as a corporation” remotely as from the US state of Montana is very easy.
As I read through this it sounds like you want to keep the car and I'm empathetic to your situation.
It’s a problem that if I overcome will be well worth it.
I see that in the center of Indiana, I'm not exactly on your route from Teulon to Peurtos Morelos.
But if a boat ride from Florida to Puerto is available, that changes things?

I might be having an indoor parking spot opening up this fall, if so, it is likely for 6-9 months.
There would be many details to work out, first of them relating to insurance (my homeowner's and your car's).
And leaving your car in the custody of a stranger, you'd need to be comfortable with that, that's discussion #2. (I'm a bit nervous to offer this, too).
If you want to discuss send me a PM.

Do you need a/c in Mexico?
That's a long trip for a vintage car to be driven and it will take a beating. Who is going to make any needed repairs on the way? And parts availability?
Buy an enclosed car transport trailer for storage both before the trip and after as well as shipping the car? Then sell the trailer when the car is safely garaged at its final destination?