I tried flying out of ORD, IAH, EWR, JFK - none had availabablity on anything other than US, UA, CO, etc. and again - the price was within $5-$10 - so not worth it.
Last weekend I flew on ANA from SEA to NRT to try the new 787 and their charges were almost as high as AC doing YYC-NRT. Not all the other airlines have lower rates.
But I do know where you are coming from as I usually do try to use metal other than AC or LH on overseas legs.