UPDATE:
Check USPS for Priority Mail Express. In some cities there is holiday pickup and that provides for 1-day delivery. Cost is $25.50. If Los Angeles either picks up or there is an acceptance location in Los Angeles which is open today, you can have the passport tomorrow in good time for your Friday departure.
I see that the 8:00 AM delivery via Fedex on Friday won't suit. On the other hand, AA has a later flight with a 6:29 PM arrival into LAX. That drops your connection from 10 hours to 2.5 hours which ought to plenty of time, particularly because you won't have the detour to pick up the passport while on the ground at LAX.