here is another plan..
call the fla dmv, let them konw that you are putting a different frame on your truck, due to damage, or whatever (this is sort of what you are doing. the key being that you do have titles to both trucks that you have.)
tel them that you were made aware that sometimes the frame had a vin # too. ask them if you need to get your new frame inspected(the bureaucrats will see $$ signs when you ask this
)before you install it on your truck.
the key to all this is that you do have 2 titles, and have both trucks in your name.
most people only have on title, and it is usually for the one they don't want.