White buildup on tile at water line, help!

I had this white line exactly as you described it and tried every chemical I could think of - nothing had any effect. I could remove it with a razor blade but it was so difficult that it was not a practical solution. I finally solved the problem using an Aussie product called Rok Blok which is like a pumice stone but is softer and artificially manufactured from crushed glass particles. This worked remarkably well and did not scratch the glaze. Unfortunately your tiles are not smooth and glazed like mine so I am not sure how well this would work for you. The downsides of this rubbing block were the expense (about $10.00 AUD each if bought in a pack of 10) and the fact that they wear away quite rapidly.
 
Found something that worked for this problem. Ended up using Jack's Magic Tile Plus Stuff and moderately scrubbing with a 3M Scotch-Brite pad. I left the liquid on the tiles for a couple minutes, scrubbed the liquid into the tiles thoroughly, let it work for a couple more minutes, then rinsed. It's not a fast process--I did about 8 tiles at a time. The tiles weren't quite perfect when I was done, but I'd say it was a 90% improvement. Hint: use a condiment squeeze bottle to apply the tile cleaner.

Before/after picture attached.
 
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