I have a friend who has an accordion (don't know makes and models and such, but it was a regular sized piano accordion). For one flight he removed the accordion from it's case and packed the case with his clothes and such and had that checked in. He wrapped the accordion in bubble wrap, keeping the straps free, and carried it like a back pack as his carry-on. He had no problems fitting it into the overhead compartments that way. Although he did have to make sure no one tried to but their carry-ons on top of it.
I can't recall what he did with his clothes and stuff once he reached his destination and put the accordion back in it's case.