I'd like some help in determining the best chemical/tool to use to clean our tile.

Here's my typical chemistry:
Free Cl2 6.3
Combined Cl2 0
pH 7.3
Alkalinity 56
Calcium 193
CYA 79

I can't post photos, but the build-up on the tiles is thick white (calcium-like) and the grout has been darkened.

I've used Muriatic Acid in the past with a hard pumice tool, but it didn't seem very effective.