I have travelled to Oz a couple of times in the last 3 years and used open jaw connections both times, also with layovers in SIN and HKG for 4-5 days each way.
I used Traifinders in Manchester both times, and found them reasonably priced, professional and helpful, even when changing itineries due to wife's disabilities. Phone 0161 839 3434 - and I'm not connected with them!!