parabellum -
I would tell original check in that I intended to break my journey at LAX
That might be the easiest option but it'll cost $25 to do that. Not a lot of money relative to the cost of the ticket but since this is an international trip on one booking with AA I'm not supposed to pay that charge and have not had to deal with this until the codeshare agreement between AA and BA.
As I said previously, I'll let the LHR BA agent do what they did before and then see if I can still check the bag the next day with the original tag still attached. I'll report what happens.