You have 60 dives under your belt. The big question I would ask regarding those dives that you've conducted is what variability was there in the environments -- if you did 60 dives but they were all in Vortex your experience is not going to be as well rounded as a guy that has only completed 30 dives but they include the ocean, quarries and springs.
You've already got nitrox under your belt, that's highly applicable. With the exception of the deep dive, there's not much that is taught in a standard AOW course that is applicable to cave diving. However, what should be applicable is exposure to different environments because that will simply help make you a more rounded diver and more comfortable when dealing with new challenges. Sadly, not all AOW courses are taught with the idea of exposing divers to different environments and many are really just a waste of time, so signing up for an AOW course may be pointless depending on who teaches it.
You've stated your goal is to become a cave diver and you've put some time into diving. A cavern course may be a reasonable step, it is a recreational course and not a cave diving course, but it will introduce you to cave diving concepts and the overhead environment, plus give you practical skills that are applicable to cave diving when you're ready.