Ah okay, think I have it sorted now. If when I first fly out, I don't stop over in NRT, I can do the SIN and NRT stopover on the way back.
This is what the trip looks like now, and validates in mileage monkey:
MNL-NRT-HNL-LAX,SEA-ORD,DCA-DFW-MEX-MIA-LIM-SCL-GIG-LHR-SIN-NRT-MNL
Now to sell...