Northern hemisphere summer - is this the big one? (Weather)
Wow. If I let the yard go around the house in Florida, it, the house, would disappear. Is this a somewhat dry area? It sounds like it. So you're in a pickle. Cows or grass. Shit. Well, you have lots of that too.
So I assume this introduced grass is in the area, and even if you were to eradicate it, it would reseed naturally. I'm beginning to appreciate the couple of acres of wooded land we still have in Florida, so thank you for that. But that doesn't solve your problem of course.
Have you talked to any locals and gotten their advice?