Well it turned out that my cork floors could not be sanded. They were cured with some sort of oil. The plan now is to wax them with a heavy dark-tinted wax. See the sample spot in blue. I think it will be cool and almost leatherish when I am done.
The bedrooms' cork floors are going to have to be ripped out and replaced. The cork was too damaged by the tack boards for wall to wall carpet.