I am flying DFW-SFO-SYD, first leg on AA, second on Qantas. Picked SFO over LAX as I can get a first class seat for a business ticket as they don't sell first class now.

Ticketed in Business, Qantas Platinum / OW Emerald.

On the Qantas web site they say to use the JAL lounge and it is open from 19:00 to 23:30.

My AA flight arrives at 17:30. I noticed that there is a BA flight that leaves at 18:55, which means the BA lounge will be opened. So should I stay in the AA lounge after getting off the domestic flight, or head over to the International Terminal and hang out in the BA lounge until I get chucked out then go to the JAL lounge?