Well the basils are annuals and are quick and easy to start over. Personally, I wouldn't bother trying to bring them. And I know, because I am getting ready to move also, but only from zone 6 to zone 7.
Your perennial herbs are worth taking with you. How well they will survive will depend partly on when you move. If you move in the summer, the difference between the weather in your FL garden and the weather in your NC garden won't be that big. If you move late in the season or in winter, they will be moving from warm to cold and it will be a tough transition.
I wasn't familiar with Cuban oregano, so I looked it up. Stuff seems to have a million common names and judging by them, no one really knows exactly what herb it tastes like or where it comes from (except some place warm!) Common names include: country borage, French thyme, Indian borage, Indian mint, Mexican mint, soup mint, Spanish thyme, big thyme or broadleaf thyme, Cuban oregano, Mexican thyme, queen of herbs, three-in-one herb, allherb, mother of herbs, and so on. It is in the coleus family and unlike regular oregano, is only hardy where you are, zone 10.
So that and the rosemary will have to come in for the winter in your new garden. I would start by potting them up right away, so that they get used to being in a pot. I don't know about the Cuban oregano (Plectranthus amboinicus), but the rosemary likes sandy, slightly alkaline soil and will do better in cactus mix than regular potting soil.
The thyme should be hardy in your new garden in NC, if it has a chance to get hardened off to the cold gradually. Best wishes with your move! Since I originally moved to my zone 6 location here, from zone 10b in So. Calif., I will testify that the transition will be at least as difficult for you as for the plants! I've now lived here more years than I lived there and I still hate winter! Keep us posted how it is all going for you. ...