I think I found a good solution for the seatback tack strip. I ordered a strip of Low-Density Polyethylene from McMaster-Carr. A 3/8″ x 2″ x 48″ chunk of LDPE was only $7.50 plus $5 shipping. And it came the next day, packed in a nice sturdy tube that probably cost more than the shipping charge! This material (the stuff that gallon milk jugs are made of) holds tacks well, and it is tough and flexible. I cut a couple of 3/8″ x 3/4″ strips, and drilled screw holes in it. The ends need to be rather curved, so I dipped them in boiling water to get them soft and bent them to the correct shape as they cooled. Besides the LDPE, I had also tried a piece of that “plastic wood” that is used to make decks, and it did not hold tacks very well.
I also got a lot done on the wooden seat base frame. I needed to make a sort of tongue-and-groove joint on each corner, and I had no idea how to do this without some sort of specialized machine tool. I did a bit of Internet research and found that I needed to make a “corner bridle joint“, and I learned the correct trick to doing it with a table saw. The joints came out nice and accurate. During the next week I’ll do some more carving, cutting, and drilling to get the frame finished.