How to clean stubborn stains from pebble flooring in shower?

My grandparents installed stone pebble tile in a large open shower nearly 50 years ago and as they aged, it became pretty neglected. My husband and I bought the house a few years ago. There was a wooden Japanese furo in the corner and there is an outline stain on the floor that looks like rust/iron/lime/calcium build up. We've tried bleach, baking powder & vinegar with lemon, hydrogen peroxide, Lime Away, and lastly Bar Keepers Friend. We have not tried CLR yet as Google told me that Bar Keepers Friend was more effective. Bar Keepers Friend did work best on most of the floor tiles and grout (with a significant amount of elbow grease), but what is left is making me fear there is no saving this floor tile. We'd really like to save it and I'm hoping someone can provide a solution. Any ideas? I have a picture if it would help.