No, AA did not "fob" OP off.

His flight was so delayed that the trip became in vain and he was entitled to a refund. He accepted the refund and that is the end of it. The AA agent's hypothetical.

AA cannot award another carrier's points/miles, e.g. avios & TP's and thus OP must address that request to BA. It is highly unlikely that BA will grant the request, but there is none other than BA to do so.

The agent was correct that had OP sought AA miles and other credits, it would have been within AA's power to have granted those as a customer service gesture (original routing credit), but when AA evaluated these facts it is unlikely that OP would have received much if anything.

One question - WN flies the LAS-LAX hop with 11 frequencies per day with a ticket price of between $50-70. Given the importance of the run to OP, would it not have made sense to jump on one of the WN services and take the refund of just the first segment of the AA ticket? It is entirely possible that under those circumstances, BA might have granted the ORC for that segment. But, if BA did not, making up the single segment is a lot easier than what OP now faces.