Thanks both for the detailed advice, it is really helpful and much appreciated. Given all this information, connecting to AS in T6 definitely seems like the better option over connecting to the AA Eagle's Nest via T4/T5 - I'll opt for the AS flight.
I will have checked bags and hopefully they will not take too long to show up, but if not I am hoping that with several remaining AS flights to SFO/SJC scheduled for later in the day, rebooking shouldn't be an issue if I miss my original connection due to Immigration/Customs/Baggage wait times.