Use Florida. You are now allowed to elect this thanks to the Veterans Benefits and Transitions Act of 2018 (PDF in link). This law, passed in December, allows the non-Active Duty Military Spouse to claim the Active Duty spouse's HOR even though you might never have established residency in that state. Since Florida has no state tax, you will want to make the election to have Florida be your Home of Residence state as well.
To recover the taxes withheld, file a tax return with a zero income for the state in question (whether it is North Carolina or the state where your spouse is stationed). Mail in the return (do not e-file), and write across the top of the form wording such as: Per the Veterans Benefits and Transitions Act of 2018, I elect Florida as my legal state of residence as a Military Spouse under the MSRRA. That state will have to refund all withholdings for the year, because you are now only taxed in Florida for state taxation, and Florida has no state tax.
Inform your company as well of this provision so that they stop withholding any state tax from your income. As long as your spouse is active-duty, you will not pay state taxes unless Florida adopts a state income tax.
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