Very Strange.. I know that is the law in South Carolina , Tennessee (well not anymore, they have Constitutional Carry) and some other states, but was told it was not the case in North Carolina. I specifically talked to the Attorney General/DOJ and Cabarrus County Sheriff about this. I might say call Cabarrus county Sheriff and ask to talk to the Deputy who is an NRA conceal carry instructor. He is very knowledgeable about these laws and teaches the CHL courses.
The laws you quoted are still vague with how they apply to a resident who has a non-resident CWP permit. From what I see there it states that you are allowed to conceal a handgun permit and that no other weapon but handguns are allowed with such a permit. That would make a NC permit, a CHL vs CWP. The other law you state 14-415.24 just states that NC recognizes out of state conceal carry holders as they would be NC residents with the laws where they are allowed to carry.
None of the laws mentioned specifically state if you are required to have a NC carry permit to carry in the state as a resident. I read word-for-word in the TN and SC state law where it specifically does state that. From what I gathered, if you have an out-of-state permit it is recognized, but you are basically treated as an out-of-state resident carrying in the state. You cannot buy a handgun in the store with that permit. Since NC does not have pure 2A rights for handgun purchases.
Again, I think this specific Sheriff department could be wrong unless the law recently changed. I'd call Cabarrus County Sheriff and then make a call to the NC Department of Justice office when they open and hear it right out of the horse's mouth. I never trust any one Sheriff department to give me the correct laws, especially with confusing laws as North Carolina has.
That being said, you definitely should get the permit of the state you are in, even a Constitutional Carry state, in my opinion. It just has many legal benefits, especially when travelling and for handling those uneducated LEOs who may not know the laws themselves when they stop you.
Yeah, your FL is definitely a valid permit , it just becomes a non-resident permit.. I have about 3 of those now

. My TN CHL is deactivated , unfortunately, since they don't recognize non-resident permits.