Thank you all for your help, it is much appreciated. I think I'll look into the car hire / day rate hotel room and see what I can come up with. (Southwest timings aren't much better, and there's no reward availability from LGB). Failing that I'll just make sure I've got some good films on the laptop and stock up on G&T in LAX lounge before leaving!
I had thought about just not collecting bags from baggage claim, and going back a few hours later to track them down saying "I forgot", but I guess that's a bit risky/not advised!
Thanks again