Four coats of finish were smoothed on over the course of the weekend, and I believe there are two coats left to apply. (Dakota decided to do extra coats since the kitchen is such a high-traffic area.) We ended up going with AFM Safecoat PolyureSeal BP, which I purchased at Architectural Coatings + Design Center in Tarzana. I found them to be very helpful and accommodating in terms of the finishes and amounts I needed.
After doing some online research, I decided that AFM Safecoat was the right choice for us. It's a water-based clear finish with very low VOC. It's also LEED qualified and contains no formaldehyde. I got a gallon of gloss and a quart of satin. Safecoat isn't cheap; the gallon ran me about $100 and the quart was about $30, but I think it's worth it to have a less toxic floor.
According to the directions, for a satin finish, you apply several coats of gloss first, followed by the satin. Here's an image of the first coat going down, after a thorough floor sanding by Dakota.
The smell from the Safecoat PolyureSeal BP was fairly strong, but dissipated after about an hour. I've never refinished a floor before, so I can't really speak to how the odor compares to other polyurethane finishes. I do appreciate that the odor doesn't linger after the finish dries.
So far, the new floor looks great. The finish is shiny and smooth, and the transition between the old floor and new floor is noticeable but not distracting. Predictably, I now want to refinish the floors in the whole house. But I think for now we'll have to focus on the kitchen. (One project at a time!)