Ted, wood fires definitely aren't allowed except on the beach but, after seeing your post, I called the Park Service HQ at Hatteras to ask about propane
campfires. Spoke to three people and have a 'don't know', a 'probably' and a 'pretty sure they're OK if you can cook on them'. The last was from LEO and he said he'd check further and call me back with an official ruling.
I just bought a camp-fire-in-a-can which does have a grill rack feature so will plan to take that if I get an OK. We're coming up your way (Pisgah NF) Easter Sunday for a few days and purchased the CFIAC to use there because of the firewood restrictions.
I'll post back with the ranger's official response.