Bioacidification can take out your buffer if your buffer isn't replenished and that definitely can stall out a cycle. 25% weekly water changes with 5dKH in the tap should be sufficient to replenish the buffer. This is one of the many good reasons for regular water changes.
It seems odd to me that the ammonia level in the tank is the same as the baseline tap. It also seems odd to me that the ammonia in the tap is that high. I'd start by taking a water sample to a Local Fish Store and asking them if they could test it for you to confirm that its not just a bad test kit.
I think that either test for ammonia reads total free ammonia but will not read chloramine. Not 100% sure on that, but I think thats the case. Are you testing the water straight out of the tap or in the bucket, after its been dechlorinated but before you've added it to the tank? The dechlorinator may be giving you a false reading. Is it always .6? Does it change between water changes, high at change and then fall off? The plants should be taking up at least some of it.
If your test kit has 1 bottle of chemical its a Nessler test and the false positive is more likely. A salicylate test will have two bottles. It will say on the box.
Decaying plant matter is a source of ammonia. I'd remove any that you see. Live plant matter will take up ammonia. Fast growing plants will take up a lot, slow growing not so much. If the plants are eating all of the ammonia, you may never get many nitrifying bacteria. Slow plants may share with a small colony. Be careful about yanking all the plants at once. Something needs to be in there eating the nitrogen.
Nutrafin Aqua Plus, according to their own website: "… gets rid of chlorine (and chloramine) as a function of its purpose. It will not remove ammonia as part of the operation…." I confess: I'm dumbfounded. I'd use Amquel or Prime or at least something that handles Chloramine and Ammonia. I can't believe they sell something that does one and not the other. That could be your source (Amquel and Prime will still test positive with a Nessler kit, they just won't be toxic).