From SFO your easiest routing is probably via SEA or DEN, connecting to Icelandair. They are also starting PDX a few days a week next summer.

Iceland is poorly served by the alliance carriers. I believe that DL's flight from JFK is the only alliance option from the US. A few of the Euro carriers fly to Iceland, but generally from their secondary hubs.

Generally speaking Iceland is a small market and Icelandair covers that market very well. This is a destination where it makes sense to forego trying to earn any miles, and just go based on price/convenience.

As an FYI, AS used to partner with Icelandair but I believe the partnership ended.