I live in an area with very hard water. I mean, super fucking hard and with a high pH level. Currently, I keep African cichlids which love the water conditions here, but I didn't always. I actually used to successfully breed angelfish, which love soft water with a low pH. Anyway, here's my opinion on it.
Yes, peat moss in the filter does work. It's quite effective, however the peat leeches into the water and stains it brown. This is healthy. You might not like the darker water, but it's fine for the fish. They don't care and that's how their water would be in the wild. The best way to do it is to get a reverse osmosis set-up. They're a bit pricey though, but the water will be crystal clear. If you go with peat moss, it would go into a filter bag (you can buy these at a good pet shop) inside the filter. It works best with a canister filter (IMHO, the only decent filtration system aside from wet-dry), but you could probably do it with a HOB filter, too.
This site will explain water hardness a little bit more:
http://www.drhelm.com/aquarium/chemistry.htmlAs for the 20ppm nitrates, that's okay, but don't let it get much higher. Here's a site on the nitrogen cycle, it will explain it better:
http://www.thetropicaltank.co.uk/cycling2.htmAnd overall, thekrib.com is one of my favorite aquarium sites.
BTW, how big is the tank, what's the filtration set-up, and what kind of fish are in it?