When driving through New York, and New Jersey on your way to North Carolina I would be EXTREMELY careful. Even though you are fully FOPA compliant, getting nailed there with gear in the trunk could cause you some serious hassle. Check the NY/NJ forums here at OC.org for more specific information.
My best advice when driving through these two States is to make sure you obey all motor vehicle laws, and make sure your vehicle is in good working condition (with all the lights functional, etc.). Don't give anyone a reason to pull you over, and just soldier through their jurisdiction while being fully compliant with all Federal firearm transport laws.
If you plan on carrying versus transporting after running the NY/NJ gauntlet, I would encourage you to check with the nraila.org site to determine what the carry laws are in the States you intend to carry in. Obviously, research your own Utah Permit reciprocity pursuant to this.