Just to avoid the TSA, I would pick the Eagle shuttle (follow the signs to Gate 44, down the escalators). All you have to do is show an AS BP or printed itinerary. The Eagle-T4 shuttle runs every 5-7 minutes, and Eagle-T3 shuttle every 10-15 minutes. When you get to the Eagle satellite, tell the person with the radio that you want the shuttle to T3.
Also, I would suggest seeing if AS SFO can print out your onward BP. Finally you can also call AA to get your AS PNR to do OLCI with AS... I've had good (but not 100%) success with this.