A year ago, it was reported here that QF would grump at AONE'ers on those NA transcons, but didn't police the flights aggressively. A couple of weeks ago a res agent - for BA, iirc - mentioned here that QF now will send a grumpy message to an airline whose rtw department us so bold as to book QF107/108, and of course cancel the res. So I doubt it's worth the effort.
Unfortunately, AA's 3-class 762's are not even close to the same class - even their intercontinental 777's are barely comparable - and AA is about as unwilling to give up seats to A pax as Qantas is. I've never seen anything but A0, and Yield Management certainly doesn't fall all over themselves accommodating a request from the rtw desk, although others have reported successes. Maybe ExPlat helps.
The only decent ride across the country is the Cathay JFK-YVR service, a bit out of the way if you're heading to LAX, but certainly a treat.