As a fellow pro flying with a horn I’d add step 6, and that’s the Jedi mind trick at the gate. Immediately ask the attendant something, or compliment them on something or just flip their attention so they don’t look on your back. You know, “Hey, miss, I’m really unclear about using my iPad on the flight” or whatever, and they’ll say it’s cool, and then they’re already subconsciencely giving you a “yes” about something whilst validating their authority and knowledge. And if your sax is on your right shoulder always go in the left line so their line of sight is blocked by your body. And turn and face them when you walk away so they never have clear line of sight to your back. It’s stressful though man, I feel you.
I have taken my tenor on a few flights and having put it in the overhead locker with other people cramming their cases in is very worrying. On that occasion I was offered a space behind the very last row of seats and the bulkhead where it fits perfectly. When I board the aircraft I always ask for it to be put in that space and so far nobody has objected.
Thanks for the advice! Next time, I will tell the airline I am playing in a famous concert hall the next day but flying in economy to stay under radar !