I have one of the ATA Anvil Flight cases, and have used it to check my accordion as baggage several times. The accordion always came through with no trouble, although there are a couple of nice gouges in the case. But, that just proves that the case is doing what it was designed for.
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.