I'm glad Loman got to this post I had trouble getting on the forum yesterday.
IMO from what you have said I do not think you have a problem only a wrong conclusion.
When test results between tap and tank are "goofy" <- highly technical term

Nine times out of ten a factor has not been taken into account or overlooked. In this case ammonia (a nitrogen compound). Without getting seriously technical...You use a dechlor chemical to make your tap water safe, you have been using a chemical agent in the filter to "deal with" ammonia. You have fish and are feeding them, fish waste and the action of bacteria on uneaten food produce ammonia.
All of this nitrogen is being bound up by the filter agent and dechlor agent into Ammonium which is a relatively non toxic form of ammonia BUT STILL IS MEASURED BY YOUR TEST KIT AS AMMONIA.
That is known in the hobby as a false positive.
Oh...I think your Nitrate readings are a little high for a non planted tank. A couple of back to back 25% water changes should help that.
Jay