It's irrelevant given the OP's situation, but out of curiosity, I looked up the minimum connection time from International to Domestic at SFO, and it is 1:45 -- which means that it wouldn't be possible to book this on one PNR. Even then, I wouldn't recommend it due to all the variables (flight delays, baggage delivery, immigration, security lines are all unpredictable).

OP, I can't address the issue of checked bags, but your proposed 3:15 connection is starting to look reasonable, although it still doesn't leave a whole lot of room for delays of any sort. I'm currently travelling on separate tickets, and I booked a 5-hour connection, just to be safe (and in my case, there are no immigration or baggage issues to contend with).