ex-LHR is pretty tricky. I did analysis of various routes last year and found most pretty mediocre.
Royal Jordanian, Finnair, Malev and Iberia have 2 hop services ex-LHR. In particular you may want to have a look at Iberia and price up various destinations in the Business cabin. There are some places that were pretty reasonable when I looked last time.
HTH. Sorry I can't be more specific, as I'm not currently tracking good fares ex-LHR.
Oh, and if seeking the 4 QF flights/year, you may find benefit in catching a train to MAN/EDI or several other UK cities and then picking up a QF codeshare back to LHR, then over to SIN/BKK etc.