last year i was trying to get on board with the soft case
but this awful spanish airline company Vueling took it to luggage cabin
promising me that everything will be OK.

after landing in Mallorca (had a connection in Barcelona)
the stick was LOST !

eventually they found it and i got it the the day after.

flying back they had the nerve to charge me for 90 euros for "special care"

anyway it was carefully wraped with bubble wrap+towels on both sides

may consider buying this GPS device

This time I was told by SAS that I have to check the stick in on both ways. No matter how many times I was assured by the airline reps that they understand that this is a musical instrument and that it will be handled manually, I ended up receiving stick on the luggage belt.

I guess they might actually handle it carefully as promised when loading the first flight leg, but then the second (transfer) airport staff move all the luggage (including gate-checked) to the second flight as regular luggage.

Anyway, thanks to the plywood case, the stick survived the travel. The stick moved inside the case with its foaming "as is" (I guess the case was dropped from significant height), so on my way back I cut some foaming from the middle of the case and placed it at both sides of the headstock to prevent it from moving from side to side.

P.S.: on the LA-Stockholm leg there were two guys with huge acoustic guitars in gig bags as cabin luggage. How did they manage to do it?

Airlines (european) allow guitars (and sticks) as cabin luggage as long as they're in soft bags. If you have a hard case, you're out. I always travel with a gig bag (the stick being my one and only cabin luggage) and never had any problem.