Having flown with my Siwa & Figli Cobra Grande a few times (4/5 120bass piano), I have never split it for flying. Comes with me as carryon.
I do, however, make sure I'm on a larger plane for the trip, so it will fit in the overhead in its soft case, and I ensure that, whether by flying comfort or having an airline CC, I have early boarding, and try to ensure I've got a comfortable amount of time between legs. I use that to ensure I'm early in my line when there's space in the overheads. If all else fails, I've got a couple big "Fragile. This side up," signs to pin on if I get real stuck and have to gate claim check it, and worst case, insurance. Haven't needed even the signs.
If you do, remember to put it on it's belly with the buttons down. I should maybe put the cardboard under the bass action in case it goes to gate claim check, but haven't done so. I've trusted in that case I should at least be able to talk to whoever actually does the stowing underneath about the fragility and risk of incorrect positioning.
Fun story: a friend was traveling with her accordion and once the security folk were questioning it. They ended up asking her to play to demonstrate it was a real musical instrument and not something strange.