Messing around with water is a very slippery slope. Unless you are on well water or in a district that has really hard water and wacky pH levels, a decent under the counter water type filter to remove chlorine and sediment should clean up your water enough to make most beers. There is a lot of chemistry involved in water doctoring and it is not all straightforward and you could be just chasing a ghost anyway.
I've always attributed that "homebrew" taste with sanitation issues. That is the easiest thing to screw up - been there, done that. Change out your plastic hoses. Get a new fermentation bucket (or better yet, ferment in glass). Clean up your brewing/fermentation area. If it smells musty or mildewy, you've got some work to do. Pick a good no-rinse sanitizer and use it religiously. Try brewing some non-descript beers styles and concentrate on sanitation to see if you can't purge the "house twang".