After spending two hours laboring over just one 12ft x 12ft room with grit 20 paper (the coarsest available) with a floor sander, followed by a little sanding with 60-grit paper, I am not pleased with the result.
As you see, the old polyurethane is still there in about 50% of the area. I now have the impression that if I wanted to take out the old polyurethane completely, the right tool for the job was a drum sander. This of course requires more careful sanding by maintaining a steady rate of movement.
At this stage I have no desire to restart with a drum sander. I want to move on. Does applying a layer of polyurethane at this point mean that I would see afterwards clearly the marks of the old polyurethane? I'm not sure why it was so hard to take it out. Perhaps it was too old and has hardened extremely well. The sandpaper I was using seemed to lose none of its teeth after use. It's as if it was floating over the hardwood during sanding with a floor sander. I applied my own body pressure to no avail.