When doing my previous test searches, I somehow forgot to mention/include that Avios are freely transferable between the various FFPs that use Avios as a currency (e.g. BA, QF, AY, etc) as long as the transferor and transferee are the same person...and it only takes minutes to create new accounts.
On the surface, this might sound like a minor thing, but as
guv1976 suggested, the redemption algorithms differ quite a bit from program to program.
As such, I have now run new test searches on the same route (ORD-LAX, July 18, economy class) using AY and QF.
Unfortunately, AY came up empty (I'm guessing I did something wrong)
BUT, QR revealed a pleasant surprise!
I could not get QR to show any connecting itineraries at all for this routing. And, when I switched to IAH-LAX (two cities QR itself serves), I was only shown "connections" via DOH (i.e. basically an open jaw ticket from the US to DOH), which obviously isn't relevant.
Still, that 11k price is a really nice find because if you simply do one more free transfer (i.e. Chase to BA and then BA to QR), you unlock ~30% more value from the exact same Chase points. We've talked about this a little in the past on FT, but not in a lot of detail...perhaps, we should keep it that way.