One more thing and this one is a question. Is wood fire soot an issue for TSA inspection? Will it maybe trigger getting unpacked and everything swabbed? Will anything sooty get confiscated? My bet is nothing would get confiscated, but I am less sure on whether it might trigger a close inspection. Having to clean a woodstove and pots to the standards that you need to clean liquid fuel stoves would be a pain. Having a detailed inspection on every or even more flights would as well.
Sorry to go on and on without really giving the op the answers they asked for, but this is a topic that interests me and raises a lot of questions.