That's a tough one. There are tools to remove the grout in the grout lines, but I don't know about he grout on the surface of the tile. I know that there are some acids that can be used to remove grout haze, but that's a lot more than just haze!
I would ask at the pros over at the John Bridge Tile forum for advice.

I will do that but could you clarify. The tools that are strong enough to remove the grout lines - are they several hundred dollars? Or is there something I could use with my drill? I'm pretty strong but nothing I have puts a dent in the grout. It will take some kind of really good saw. I could even put up with the two or three places that have grout on the surface if I could regrout the rest of the shower floor. Thank you so much for your response. I was afraid I wouldn't get an answer.

Ask at a hardware store or home center for a grout saw. It is something that you use by hand. Or, if you have a dremel type tool there should be a special attachment for that. The problem is that with either method it is very easy to chip the tile. But I think that it would be easier to tear out and replace all the tile.

We have several companies here in Silicon Valley that clean or remove and replace, or even change the color of grout. See you have any of those locally, and if you can get a free estimate and go from there. Dremel tools aren't real expensive and you can do just about anything with them, so they are a good thing to have around, like a hammer and chisel are.

I think you should heavily chlorine the whole area and seriously consider replacing all of it. It might just be more work and $$$ to remove and correct the problem, than to just rip it all out and start over.

Good luck.

-Babka