Thanks to everyone for your replies. I guess this is an unusual situation so will test it on my next trip by leaving the baggage label on my bag and seeing if AA will accept it when I check in after a night spent in an LA hotel.
Hartington seemed to understand my question more than most and appreciate your reply. I'm really not willing to leave my bag overnight with AA or any airline, plus I want what's in it for the hotel stay. If I end up having to pay the charge for domestic checked bags so be it, but would rather not especially as this is an international trip on one booking and I'm not supposed to be charged for luggage according to AA.
This used to work smoothly with AA before they merged with BA. An overnight stay didn't present any problem, I just checked the bag in the next day with no charge as it was all part of the same trip.
I hope they get these sort of things sorted out in the near future (the super-friendly BA agent I spoke to on the phone assured me they will). I've also given up on trying to assign myself a seat on the BA flights - the website just keeps giving me an error and no-one at BA is able to help. I'm not calling AA - not worth the hassle.
Thanks again for the replies.
PS. As for booking seats, yes, I'd rather avoid having to wait until 24 hours before the flight as the choice will be limited. For this upcoming trip I'd have rather chosen AA flights between LAX and LHR but it was a late booking and the flights were full, so wouldn't have been able to choose my preferred seat anyway.