I have zero knowledge of permitting a slalom course in Florida. I would think a Google search would provide information. It’s probably under the jurisdiction of the Dept. of Natural Resources, or whatever it’s known as in Florida. You may also have to get signatures from a certain percentage of the lake property owners. The fact that there were courses on the lake in the past, may help your chances for approval.
Does your neighbor know if the old courses were permanent? If they were, the anchors may still be in place. If you do go the portable/cable type route, you don’t have remove it, once installed, unless you’re only able to get permission for a course that must be removed when not in use. Jon Travers, obviously is an excellent source for all things slalom courses. Good luck!