Yikes! Thats some nasty tap water. It could also be the chloramines in there throwing the test off, can't tell for sure though.
I think your best bet now would be to fully cycle the tank fishlessly. Once that is complete, and you add fish of course you'll still need to do your regular water changes to remove built up nitrates and fish waste. Since your water has ammonia in it you'll end up inadvertently adding ammonia to the tank when you do a water change, but since the filter would then be cycled the ammonia will be naturally removed. It might be a good idea to continue using a water conditioner with ammonia neutralizer so that when you do have to do a water change it's not so toxic.
Edit: I was doing some research and I came across this article here. Check under the "Chloramine" heading, it has a couple possible solutions for what I think may be the underlying problem here.
I think your best bet now would be to fully cycle the tank fishlessly. Once that is complete, and you add fish of course you'll still need to do your regular water changes to remove built up nitrates and fish waste. Since your water has ammonia in it you'll end up inadvertently adding ammonia to the tank when you do a water change, but since the filter would then be cycled the ammonia will be naturally removed. It might be a good idea to continue using a water conditioner with ammonia neutralizer so that when you do have to do a water change it's not so toxic.
Edit: I was doing some research and I came across this article here. Check under the "Chloramine" heading, it has a couple possible solutions for what I think may be the underlying problem here.