AA is just not a great airline to fly to Asia right now. Service cuts made in the pandemic still haven't come back - e.g. AA is serving Japan from fewer US cities than they did in the mid-00s. If you plan to upgrade, AA via HND/NRT is the best bet. ex-LAX may have better upgrade odds than ex-DFW. You can also look into flying DFW-ICN and then flying onwards on a non-Oneworld carrier but maybe only if you could clear the upgrade in advance.

If you're resigned to Y+, JAL's product is quite good and gives you a lot more flight options. CX also has Y+ and it's ok. AA's Y+ is not bad.

Fares tend to be lower out of LAX and especially JFK. AY has often offered ~$3k J tickets JFK-HEL-NRT/ICN/HKG/SIN but I haven't checked recently. Fares ex-YYZ and YVR can be low but may require a backtrack to the US.