Just cut SYD out and it becomes a DONE3, of course with a lot less miles...

ARN-MAD-DME-ORD-SEA-JFK-DFW-ANC-DFW-JFK-HKG-NRT-SIN-NRT-SIN-LHR-ARN is a DONE3.

Have you thought of flying NRT-DEL-NRT instead of NRT-SIN-NRT? It should bring you some more miles, although not too many.

You may also add a return trip between LHR and DXB or MCT on BA which would yield more miles than going to Moscow, but would require one more segment in Europe (and consequent redesign of the whole itinerary - sthg like ARN-LHR-MCT-LHR-DFW-YVR-MIA-DFW-ANC-DFW-JFK-NRT-DEL-NRT-SIN-LHR-ARN - 51152 base miles). Mileage monkey says this itinerary is invalid because there is no YVR-MIA service, but in reality it exists (AA282).