Hope you tell all the gals to take off their high heels and offer to pay for their ruined pantyhose and nylons, Rick.
I agree that you have a real problem. You might check to see what is the finest grit paper you can get for a drum sander. A specialty abrasives store might be able to find or make belts of about 100 or 150 grit that might solve your problem. I don't know that this is the answer, just a suggestion. A floor buffer with a screen would not be quite coarse enough and probably would not do much to reflatten the floor. You could go with a regular hand held belt sander but this would take forever. Wish I had a better answer for you. You might check with some pro's or born and raised in Japan ladies. They have wood floors that are pretty soft also, I believe.