FWIW, I was on a similar mission with my TA, suggesting that she ask Qantas to ticket a trip that starts YYZ-LHR on BA and comes around to SYD-LAX on QF. Her opinion was that QF would not be willing to price the trip, for their own reasons, and although she could get BA to price it and then ticket it on QF stock, her agency would be on the line for a chargeback if Qantas disagreed with the BA pricing.
I mention this because some here have made fairly strong statements that we could ticket on any carrier that had a piece of the trip, or at least any carrier that had an intercontinental piece. That has some importance for those of us who use TA's and want to keep them happy and well-fed, as BA essentially pays zip for commissions.
So from where I sit today it looks like the story is that the first transcontinental carrier is required to price and ticket, and anything else that happens is luck or negotiating skill.
[BTW the codeshare suggestion sounds like a great one. Unfortunately doesn't help me as QF and BA apparently haven't gotten in bed together on the Atlantic.]