The FL DMV seems to have fixed my title. I got an envelope in the mail today returning all of the documentation I had sent them, but no letter explaining what had been done.
In FL, auto titles are electronic and can be looked up online so I went out to their site and checked the VIN. Previously, because of the clerical error, the VIN lookup didn't return anything. Now, the VIN pulled up with a title issue date of 1/9/2012, so it looks like they fixed it. I assume they sent the corrected title back to the previous owner, who will need to sign it back over to me.
I've been waiting to get this straightened out before really starting on anything just in case I need to take the car somewhere to get another VIN verification or other inspection by a state authority. Once I have the title back in hand and can get the it re-titled in my name, I'll take it out for one last drive, then start disassembling things to get the motor out.