I think I may have accidentally got lucky as TK loaded a bunch of indirect fares to encourage passengers to try the Turkish product from Aus as they launch their MEL-SIN-IST operation. I played a lot with their website with the journey starting in MEL and got some VERY low J-class fares (sub A$5,000) on MH and JQ.
Not sure if they are available but I set my travel agent the challenge of matching the ex-Aus fares and this is what she came up with, and I got a sector IST-Middle East for free (I needed to visit a client so tied it to a leisure trip.