I was thinking about this last night and realized we were approaching it all wrong. The real point is not jurisdiction, it is that the Oriskany is the property of the state of Florida. As such it's absolutely their right to determine how the public can use it, no matter where it is located. Arguing otherwise it equivalent to stating that anyone can take legally take the stereo out of any U.S. licensed cars parked in Canada.
The only question is whether Florida cops could arrest you on site or whether they have to wait until you cross a line x miles from shore to pick you up. The USCG could certainly report the activities to FL and even follow the boat in.
In other words... What Uncle Ricky said.