re: Any experience using job recruiters/hunters?

This is pretty spot on. The recruiter is looking to fit someone to a position of need for a specific company. They're likely not going to waste time helping you figure out what career best fits your skill set.

Someone mentioned marketing. Based on what you listed, that seems like a potential fit. You should figure out how to approach someone within that industry who can break the industry down with a broad brush. It would help you understand what career paths are possible.

On a related note...this reminds me that there seems to be a disconnect between academia and the real world. You said you were headed toward a career in teaching but now you don't know what you're qualified for. Not a knock on you. Just something I used to think about when I was younger and would run into someone with what I considered to be a very cool job in an interesting field. Always thought, man if I had known that was a thing I would have gone that direction. I grew up in public school in LA so maybe that's the root problem. Sorry in advance for the sidetrack.