Great Tips, and I also heard that Yo Yo Ma's Cello earns miles, which is a great thing.
I would also explain to the airlines that your instrument is needed for your work and must travel safely (it's just as important as laptop or a bag of beer steins... if you want an explaination on that one, let me know.)
And hey! if Yo Yo Ma can do it, maybe you can get an ff account for your tuba!