I know I'm the one who asked the question, but I came across this web page and thought it might be helpful for anyone else who searches for this topic.

Transportation Security Administration: Camping

The TSA rules allow stoves and fuel bottles in both cary-on and checked luggage as long as there are no vapors or residues present. I feel I can clean and dry my empty bottles well enough but not so sure about removing all residue from inside the stove itself. I'd hate to have it confiscated on my way up there.