So as an update, QR are refusing to allow STPC on an AA ticketed DONE3 which includes AMS-DOH-TXL, because QR don't sell a through fare between those points, despite me being around 9 hours in DOH.
Secondarily for TXL-DOH-ORD, which is 9 hours again, they will only do it on the AA ticket if both legs are QR coded. If either leg is a AA marketed but operated by QR, they won't do it. They said if I switched it back to the QR, it would be eligible.
Only problem is that the DOH-ORD QR code is now showing D0, so I can't switch it over.
Anyway, some interesting points of data in trying to work out the finer points of the QR STPC policy: Only where they have a ticketed fare, and only when flights are both marketed and operated by QR. I'm going to have some very long overnight stays in the Al Mourjan lounge in my future.