I began the stripping process with my little Ryobi detail sander. That was getting me nowhere fast. Next I went to gel stripper in a can. That took off one, and sometimes three, layers at a time. It worked best on the seat of the chair; it didn’t seem to affect the spindles. When I emptied the can, I reverted back to the electric sander. Then I tried coarse steel wool, first with mineral spirits, and second with chemical stripper. My second can of stripper is more powerful, so it seems to take off more layers more quickly.
I’ll keep you posted on my progress.