Originally Posted by christep
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.
LHR-SFO is operated by BA, toxic to the OP's quest for AA EXP.
OTOH Tom could go LHR-LAX-SJU-DFW-ANC-DFW-JFK in the US instead, which takes the total up to 63,754 mi for 95,631 q-pts. Hard to imagine one couldn't get the remaining 4369 q-pts just getting to and from WAW.