If all you have is 80 pounds of sand in a 120, that's not even close to enough for a deep sand bed capable of processing any quantity of nitrate. Plus, the grain size is really important. For southdown sized (also aragamax) you'd need at least 200 lbs. If the live sand you have is the stuff that you buy in lfs called "live sand" the grain size is a little bigger. You'd want to supplement that live sand with a lot of the "sugar sized" grains like southdown, pure caribbean, or aragamax.

There's a calculator on reefcentral (our's doesn't seem to be working) for sandbed depth/weight needed. On my 100 gal, a 4" sandbed came up needing 225 lbs or something like that.

Also, you didn't mention any fish. There's really no reason you should have any measurable ammonia, unless you have a huge fish load and even then....if you have no fish, either your test kit is wacky (likely) or you're still getting die-off on the liverock in your tank, which is also very possible in a 2 month old tank.

BTW, if your ammonia test kit is that far off, how do you know you have nitrates anyway?