I used to have some incredible stuff called, I think, ZAP, that was miraculous in removing hard water stains. I bought it at Linens n Things at least 5-6 years ago. It consisted of a bunch of wipes soaked in whatever chemicals it was made out of, and came in a round plastic cannister, kind of like a large size cannister of hand-wipes.
I do not think it is the same as the Zap! you can find by googling, and maybe the name wasn't Zap but something along those lines, like Zow or PZAP or ??? I'll try to find the cannister.
I used it on the outside of windows that had been stained by decades of rain coming through metal screens. I had previously tried everything I could think of, and even professional window washers couldn't get the cloudiness off. I was told that the glass was etched and thus nothing could remove it. However, a few wipes with this stuff, and the windows were completely clear.
I even took some before and after pictures with the intention of sending them to the company - they are amazing. Unfortunately, I can't find it any more.....
If you can find it, try it on the inside of your shower doors - but definitely wear rubber gloves, it's powerful stuff!