rl, the question you don't seem to touch is whether you truly are a Florida resident as defined in the Florida Statutes:
Statutes & Constitution :View Statutes :->2000->Ch0222->Section 17 : flsenate.gov 222.17 Manifesting and evidencing domicile in Florida.-- (1) Any person who shall have established a domicile in this state may manifest and evidence the same by filing in the office of the clerk of the circuit court for the county in which the said person shall reside, a sworn statement showing that he or she resides in and maintains a place of abode in that county which he or she recognizes and intends to maintain as his or her permanent home.
If you have a place to live in Florida, you should be able to provide a physical address that qualifies for a driver's license and voter registration. If you cannot provide a RESIDENTIAL address where mail can reach you--well, that's reason to challenge your claim of "residency" and refuse to register you to vote. You can register to vote at the same time that you get your driver's license, all that you will need to show is usually two pieces of mail addressed to you, at your residential address.
You'll need to register 29 days in advance of an election in order to vote in it, the cut-off is October 6th this year for the general election.
Of course, that may complicate anything you have registered in NC, including any other driver's license, insurance, and so on. Multiple residency can be a can of worms.