With a quick bit of fiddling around I came up with this routing, which seems to meet your requirements for the compulsory stops (although SWP is in a different order) and comes in at 62380 base miles.

WAW-LHR-AUH-LHR-SFO-BOS-DFW-ANC-DFW-JFK-HKG-BOM-BKK-HKG-AKL-MEL-PER-CNS-SYD-LHR-WAW

If you start in WAW you do have to finish in Poland.