Worst case scenario: you take it to the ticket counter as checked luggage; they actually measure it, and so it goes 1" over. So you pay for "oversize" which isn't going to be a big deal.
Technically, on American, that really is a worst-case scenario: If they strictly follow their guidelines, the fees would be right around $300(!). They state that oversized bags are subject to two(!) extra piece fees of $150. But I doubt anyone would measure.
The owner of the instrument checked and found that using UPS to send it to Hungary would be somewhere around $500. I imagine DHL would be in the same ball park.
-Arle