If you are diving single tank backmount you will have better luck at Vortex or one of the open water shops in Panama City Beach or Destin. I would think Vortex can hook you up. Edd or Rob up in Marianna will mostly have doubles setup.

Vortex and Morrison are your best cavern dives. The river backs up over the opening to Morrison and you would have almost no natural light. There are a few other small caverns closer to Destin but they require a boat. You could rent a canoe and go to Cypress Springs as it is a nice open water / small cavern dive but it might be blown out like Morrison. The canoe / kayak rental places around Vernon could tell you that.

Vortex has a small dam in the spring run that helps keep the tannic water out. There is Devil's Hole on the Econfina but it is a sinkhole with a sidemount cave off of it. Honestly Vortex or Jackson Blue will be your best options