I strongly urge those in these types of situations to publically tweet about the issue. "AA canceled my flight, replaced it with a BA flight and refuses to put me on it without increased charges for me. Help please." or something similar. Then from there on, you can direct message the twitter team. The twitter team seems to be able to make things happen that even managers on the telephone cannot.
After JFK-HND was canceled I had one heck of a time trying to get to Japan over New Year's. AA's call center basically said "find whatever is open now in October, or take a refund." After using Twitter, they finally put me on PHL-ORD-NRT even though award space was not available at that time. Twitter set it all up with a PNR. When I called in to pay the taxes with my credit card, the agent then argued with me to charge me a phone reservation fee. Well, the agent completely agreed with me, went to her supervisor, and still was denied. I direct messaged with twitter while on the phone, and voila, they didn't charge me the phone fee. All of this due to AA canceling a flight, so in the end they did the right thing, but without twitter, it would have been a lost cause.