I continued my experiments with rubber bands. The picture shows the middle layers of soles made of two layers of cardboard glued into the correct shape, and leather insoles with additional leather pieces glued under them to guide the straps.
I put an insole against the doll's foot and wrapped rubber band around the foot and sole, gluing the band in place. The straps need to be a tight fit, but not stretched.
When the straps were in place, I took a piece of metallic thread, put it around the lower bunch of straps, made a knot, took both threads through a tubular bead and then around the next bunch of straps, and made another knot.
The last bunch of straps goes around the ankle and is glued to a narrow piece of leather behind the heel. I added another bead and then wrapped the threads around the third bunch of straps. Then I made a knot, took both threads back through the bead and used some glue to keep them hidden inside the bead. When the glue was dry, I cut off the extra length from the threads. The picture also shows the cardboard pieces glued in place. The soles would probably have been fine without those, but I didn't realize at this stage how thick the soles would finally be.
This picture shows better the leather strip behind the heel. The outer soles are made of leather and the heels are made of wood and covered with the same leather.
The sides of the soles didn't look very nice, so I painted them. The picture below shows the finished shoes. They are a bit tricky to put on because of the beads between the straps, but if you don't stretch the straps when gluing them, they will stretch enough and it is possible to get the shoes on the doll's feet.