After getting the right size of screws, I was able to put together the rectangle that will support the seat. A day or two later, I added corner blocks (salvaged from an old table). The next day, I brought up the legs and some of the other side pieces, and started fitting things together.
This is where the accumulated mistakes started to show. The notches on the legs were all slightly too small, and needed to be sawn larger. The seat base is slightly askew, leaving one foot of the chair not touching the floor. I will wait until the end to see how much that needs to be corrected with a shim. Adding the first of the side pieces, I discovered that I made the seat base a square instead of a rectangle, so the side pieces I had cut were all two inches too short. I cut new ones. This does not disrupt the design too much, because I will set the chair's back in later. There will just be room for a magazine rack or something behind it. The side pieces are attached to the legs with pegs; the peg holes were too deep and the pegs were too short, and nothing would stay in its place when I was dry-fitting all this together.
After taking a break to sweep up the wood chips and sawdust all over the floor and to get a snack, it was clear that the next step was to reduce the number of moving parts by gluing one end of each too-short peg in place. That is done; I will saw the other two pieces that need to be re-cut while I am waiting for the glue to dry.