There is a machine that airports use to transfer bags from one conveyor to another. It is euphemistically called 'A Pusher'. What it does is gives the bag a hefty whack "POW", so hard that it flies in the air and lands on the other conveyor. It's somewhat like hitting your bag with a large hammer.

So after you have packed your guitar, you must throw it down the stairs. If you don't feel confident enough to do that, then go back and repack your guitar.

As an alternative you can try making prior arrangements to take your guitar as hand luggage when you buy your ticket. But then you must be prepared for the fact that the cabin staff will know nothing of the arrangement. Then you will have to threaten them with legal action, demand your money back immediately and maybe even miss the flight. But enough kicking and screaming will usually get you on board. If you take that route, it helps a lot to have the guitar in your hand without a case. The sight of the fragile instrument often elicits enough sympathy with the cabin crew that they will let you on board.

Another way is to pack your guitar in one of those soft folding overnight bags that they let you hang with the coats.

I have used all three methods successfully.

Bert.