Alright, just tried calling the AA desk in the US, and they refuse to price it if neither crossing is with them. Even with much polite insistence, they told me to call BA.
I'm going to try to have TAL do it tonight (when they wake up), we'll see what they say.
If that doesn't work, would it be worth trying to book with QF, LA or AY? Do either of those have booking desks in Sweden?
Crazy idea: leave from the US. Between saving the roundtrip to Europe, and the lower taxes&fees through AA, it might just break even with the increase to 5 continents... and be more convenient too. The possibilities are endless
-Nick