Oh, gosh. You know, I just discovered this site about half an hour ago and there are so many posts to which I want to reply! I should have checked the date on this, but I'll just have to hope I'm not too late.
DEFINITELY take your accordion on-board with you. The pressure and temperature changes underneath the plane are really hard on the instrument. While it can handle these conditions, it takes it a few hours to recover, and that's if you have really good, strong wood making up your accordion and not some painted pine or something. I use a Peavy soft case 'cause it's what my dad gave me, but it really doesn't matter. Get whatever's most comfortable for you.
Oh, and I really doubt they'll tell you anything about it being too big, but if they do, just flat-out REFUSE to check it. I always do that with my guitar (obviously a lot bigger than an accordion, PLUS it's in a hard case) and I always get away with it. I tell them they'll have to insure it if I'm going to check it. They normally find room for it in the cabin after that.