OK, after reading this thread I am lost here.

1. As they are full fare tickets, cancel the QF segments and have TG book the QF segments on the same PNR. I am sure that TG would be happy to book a full fare QF ticket on TG paper.
2. It is fairly easy for a travel agent to add the QF segments as passive segments on the TG PNR which should also solve the issue.

That said, I believe that it is wrong to state that 'most' or 'many' airlines do not interline even on separate tickets, as I think you will find that most actually do, but a small and vocal number do not (BA, QF, NZ). SK even reversed its policy and now actively advertises that it will interline with any airline it as an interline agreement with (i.e. most IATA).

Where things become unstuck is that you may have your bags checked through but if you miss a flight on separate tickets (even one PNR) then the airlines will show you little mercy. As the contract is only to send you from A-B not A-B-C.