First off, I DID originally explain to the OP that they SHOULD indeed check with their OWN airline.
Secondly, when this post
I don't know about other airlines but Delta now allows passengers to PURCHASE a Zone 1 boarding assignment which would enable them to board earlier than many other passengers and obtain an EMPTY overhead bin for their instrument.
Otherwise, there is also on Delta, "other approved storage location in the cabin"
Think of all the brides who board with their wedding dresses hoping/praying that their gowns will receive a much coveted spot in the first class hanging closet.
I am NOT looking for an argument here , I am simply trying to show to the OP that there ARE options OTHER than checking the coveted instrument as luggage.
Been there done that. Dd owns a $2000 saxophone and has wanted to travel with it by air. In the end we chose not to because of the hassle. I was simply trying to share information I found in my research which helped us make our decision.
To each their own. PEACE.