Soundguy, ask AAA if they do vehicle registrations in Florida. It might be worth the $150 (???) to join just for this. (Be sure to get a lifetime supply of roadmaps too!)
Here in California, AAA offices must have been delegated authority to represent DMV back in the beginning, and they still have the ability to do registrations. I expect they can work magic if necessary to make this go through.
That said, back when was a teen I lived near the state DMV HQ. Horsetrading various cars and parts of cars, I became very familiar with the vehicle registration loopholes. My ace card was there was one ancient dragon lady in HQ, a super-supervisor over the registration clerks, who somehow had the authority to make 1 + 1 = 3 when that was the only way to overcome an obstacle. And she had a good sense of humor, of course after making a young kid squirm a little. Maybe you need to find her modern equivalent. They don't really have a goal of making you miserable, rather, you just haven't yet found someone with the authority to make this move forward.