Flying this weekend ONT-SFO-NRT, returning next Friday.

Question 1: I notice that ONT-SFO usually uses Terminal 1 at SFO. I need to get to the G international gates. Does it make the most sense to take the airside shuttle from T1 over to T3 and then walk airside over to the International terminal? Is there any other way to avoid going through screening at SFO?

Question 2: Returning, I know I'll have to clear immigration / customs and then make my way to T1. Since I'll be forced streetside when I exit customs, is the best way to get to T1 via the monorail?

I've got a 3 hour connection time on my outbound, so I'm fine there, barring delays. I have 2 hours when I return. I'll carry on the luggage and have Global Entry, so I'm hoping 2 hours will do it to make the return connection.

Any advice going either way?