There are generally more AA elites traveling from or through DFW, AA’s fortress hub. Ex-LAX upgrades are usually a bit more common.
Do you have enough miles (60k each way) to book a J award ticket? JAL gives huge value here and award space is easy to come by and one of the few remaining AA redemption sweet spots.
I often book a cash ticket in economy (or PE) to get a receipt for reimbursement then cancel within 24 hours to receive a refund, then book using miles. Not sure if that’s an option for you…