Hey now Max,
On American, they *usually* charge about $100 extra per bag (beyond the 2 that can be checked.) Call your airlines, explain your moving situation and see what the prices are. Never know, they could hook you up. When my boyfriend was moving home from Florida to the UK, he left from JFK on American Airlines. He had two checked bags plus a guitar case. Once the check in guy heard he was moving home, he just let him check the guitar case for free (the flight was underbooked as well.) So, give me a call, you never know!
I put a bunch of stuff I needed into a large box and weighed it. Came to about 70 pounds. The Post Office was going to charge almost $200 for standard sea travel and it wouldnt arrive for 4-6 weeks. Sometimes it pays to just use the airlines because they're prices are lower~ let me know how it goes.