I have been down this road (and no, I don't literally mean I-75, but if you pursue Fundies and cave training you will get to know the stretch between Atlanta and High Springs intimately). High Springs, FL is the center of America's cave diving universe--people come from all over the world to dive and train there. No need to go anywhere else. We are fortunate to be a mere 5-hr drive from that.
I agree with
@Goingforsound that if you can't afford to buy all the tech gear at once, at least buy a backplate/harness, so it's adjusted for your body. At Extreme Exposure in High Springs, you can rent a wing, regulators, and anything else you could possibly need, even a drysuit. I took Fundies in a wetsuit (5mm with 3 mm vest underneath) and was too cold--shivering on the surface intervals during a particularly chilly early spring course--but YMMV. I can relate to your statement that it may take you "a year or two" to acquire all the gear for cave diving--I certainly took my time to buy all the bits.
I would say ALL of the GUE instructors in N. FL "live and breathe caves." The question is which ones have time in their schedule that aligns with time in your schedule. Check the GUE web site for scheduled classes:
GUE class schedule. Keep in mind that what is listed is often just advertising their availability or a reflection of another prospective student's interest in setting up a class--it doesn't mean the instructor doesn't have other dates available to schedule a class for you.
If you have your mind set on caves, then you will probably want to take Fundies in the full cave configuration right off the bat: double tanks, primary light for signaling, and (preferably) a drysuit. Alternatively, you can take Fundies in recreational gear: single tank, omit the use of a light for signaling, and so forth--and you will still learn the same, uh, fundamentals, but you will then later need to acquire doubles, drysuit, and a primary light and learn how to apply the GUE principles to that configuration. I took the latter route, but I wasn't focused on caves at the time I first took Fundies--my immediate goal was simply to become a better recreational diver. Later, to learn doubles and drysuit, I contacted Kyle Harmon for a combined doubles/drysuit "primer" course as they call it.
I took Fundies with Doug Mudry and thought he was a great instructor. He has a lot on his plate these days, but he does advertise a Fundies class in March, currently with zero students registered:
Class details. That web site doesn't show Kyle Harmon having anything scheduled, but I have done several post-Fundies coaching sessions with him, and I suspect he has good availability.
Meredith Tanguay is one of the most popular and busiest instructors for Fundies and Cave. She divides her time between her home base in Hawaii and traveling all over the continental US to teach.
Lauren Fanning is another possibility, though I'm not sure if she teaches Cave 1 yet or only Fundies.
The first thing to do is contact one of them, explain your goals, get some advice, and get registered for a Fundies class.