Travelocity, LAX-SIN-LAX $691.10 TTC:

Flight: United Airlines flight 891 on a Boeing 747 Jet
Depart: Los Angeles, CA (LAX)- Thu, Oct 30 11:05am
Arrive: Tokyo, Japan Narita (NRT) - Fri, Oct 31 3:55pm
Connecting To
Flight: United Airlines flight 801 on a Boeing 777 Jet
Depart: Tokyo, Japan Narita (NRT)- Fri, Oct 31 5:30pm
Arrive: Singapore (SIN) - Fri, Oct 31 11:55pm

Flight: United Airlines flight 806 on a Boeing 747 Jet - 1 stop
Depart: Singapore (SIN)- Tue, Nov 04 6:50am
Arrive: San Francisco, CA (SFO) - Tue, Nov 04 8:40am
Connecting To
Flight:
United Airlines flight 1045 on a Airbus Jet
Depart: San Francisco, CA (SFO)- Tue, Nov 04 10:05am
Arrive: Los Angeles, CA (LAX) - Tue, Nov 04 11:31am

17,722 status miles. The same base fare applies out of SFO and SEA but the LAX routing yields the most miles.