Personally, I would be more concerned about how much time the child is gone from this state than about the term "CP". Will the child have ANY vacation time in Florida?
I have heard of the attempt to reverse custody due to the NCP claiming "defacto custody" because they have more time with the child than the CP. One NCP had every weekend plus most vacation time and proved they had the majority of timeshare. They failed to get custody because they were told that it goes by overnights, not number of hours that the children are awake and out of school.
Your case is different because you are the NCP with the majority of overnights, but if the case I recalled is a good example, it is overnights that count.
Does the title "custodial parent" really matter? Could you agree to just drop the title altogether, so that neither of you are called "primary"?
I wonder why she is so concerned. Could it be that she is holding out the possibility of returning to Florida some day while your child is still a minor?
The odds of her successfully fighting the designation while still having a minority of overnights is an unlikely outcome. However, I still think you should agree to her terms, because the possibility of her keeping custody AND keeping the child in her state is still alive.
Personally, I would agree to anything that prevents the child from being moved to the other side of the country for the rest of her childhood. If your x agrees to your terms, you have pulled off a miracle. If she doesn't, you will still probably win, but is "probably" good enough, as compared to "definitely"? It is always safer to settle out of court rather than to roll the dice.
One last thought. This may be the one concession that you need to stem the outpouring of bitterness that you and your daughter are already dealing with. What difference does it make, other than to avoid pouring salt in her wounds?
Call her Mother Superior; call her Mommy Dearest; call her anything she wants to be called. If you hear "Daddy's Home!" being squealed when you walk in the door, what does the term "CP" matter?
Make the deal.