Originally Posted by Gardyloo

Unless you were to cut out North America altogether, the price is likely the best you'll be able to do. There are cheaper LONEX fares out of, say, Europe, but you'd eat up the savings by getting to Europe in the first place (then back to CCS after.)

You can indeed add Moscow and stay within the rules - just swap PEK-NRT for PEK-HND, then take JAL's nonstop flight to DME. Note that Finnair uses SVO for its Moscow flights, so if you wanted to avoid losing a segment because of the airport change in Moscow, you'd have to fly to either Madrid or London in order to "double back" to Helsinki, but you'd still have enough segments in Europe and overall - to wit:

CCS-MIA-SFO-LAX-MEL-AKL-SYD-SIN-BKK-HKG-PEK-NRT-DME-MAD-HEL-MAD-CCS