Interesting point Jim...are classes there to teach, or to test?
Clearly, in any class, scuba or otherwise, there are elements of both teaching and testing. But, we call it a class and not merely a test.
You indicate that you would not pass this student, but never mention doing anything to teach him. Granted, he might not be able to pass the test in the same time as others, but hopefully he would learn while diving with you and end up passing eventually.
I understand the thinking behind not allowing them to enroll. I understand the value behind time in the water. But, I think there has been a shift in diving, from a mentorship to a testing mentality. Of course, your time is valuable, and the OP might not be able to afford doing 30-60 dives with you over the course of a year or two in order to gain their AOW or cavern certification, but assuming they could, could that be an acceptable way to learn how to dive well, even though they couldn't pass the test at the first dive?
OP, with 10 dives you likely do not have the skills necessary to be an advanced diver or a cavern diver. My advice is, find someone who is a good diver, and go dive a lot. Dive with several people and learn from them all. Then, look for an AOW or cavern class, and realize that not all classes and teachers are equal. Some will give you a card even when your skills are possibly sub par.
There are plenty of OW sites in north florida, and it will give you a great first look into cavern diving, if you can chat with some cavern or cave divers, watch them in the water, etc. I credit the reason I was able to move quickly into cave diving from OW diving to the fact that I was trained to OW standards by cave divers, and spent my time in cave diving shops, with cave divers, and learned to dive like a cave diver. You have a disadvantage with so few dives and not living in the area, but that is something you can change with a little effort.