+1 to the water changes. They always, always help on getting Nitrogen down.
I also recommend getting a nitrAte test kit too. That'll really help you know if your nitrites are turning as that ought.
Also, bear in mind that StressZyme is going to spike your ammonia. The bacteria in it aren't the same bacteria you'd have in your biological filter. Instead, the bacteria speed up the decay of matter in your tank, i.e. excess fish food, plant matter and fish waste, turning it INTO ammonia. This is how StressZyme "speeds up" your cycle, as the more ammonia there is, the more food for the bacteria in your biological filter.
Also, live plants really help with it. I suggest anacharis, as that just feeds off the water table and doesn't need a ton of light. Or an amazon sword, which is quite hardy. You won't even need CO2 or fertilizer for those guys.
Another thing to bear in mind is that if you've been "treating" your aquarium for ammonia, most treatments turn ammonia unto harmless ammoniUM. And test kits test for both ammonia and ammonium, meaning you might be getting false positives there. That actually happened to me... I was treating my tank and when I finally got my test kit, it registered the ammonia/ammonium as over 8! I nearly fell off my feet...
Lastly, your water may have some ammonia in it too. Try testing that to see if you're introducing ammonia naturally with your tap water.