The only *A one-stop from LAX is LAX-ICN-MNL on Asiana.

The shortest duration *A routing that doesn't go through ICN is SQ LAX-TPE-SIN-MNL (LAX-TPE-SIN is SQ29, one flight number).

For maximizing UA flying, you can do LAX-NRT-SIN and then fly SIN-MNL. You can also fly to HKG as mentioned above and connect to Cathay Pacific or fly to NRT and connect to JAL, but neither of those are *A connections.