OP - Number of "itineraries" is irrelevant. All that matters is tickets. While BA certainly may check bags across OW tickets in general and specifically across AA tickets, the sole issue for you is whether AA chooses to collect baggage fees as it is entitled to.

With a little luck, you will simply drop (and not recheck) your bags post-Customs at LAX and not be required to pay anything. If AA does snag you, you are no worse off than you should be.

On the return, you will pay baggage fees at OGG, but your bags will be checked through to LHR and returned to you there as there is, of course, no intervening border at LAX.