It sounds to me like the original tank filter has never cycled to zero ammonia, right? You are close, but not quite there. Nitrites and nitrates are looking pretty good. I would think you would simply need to treat that tank as a "fish in cycle" and be patient.
Also, have you tested your source tap water for ammonia? My tap water is 0.25 ppm ammonia. If you have ammonia in your tap water and do a lot of water changes, then you won't get zero ammonia!
Also, have you tested your source tap water for ammonia? My tap water is 0.25 ppm ammonia. If you have ammonia in your tap water and do a lot of water changes, then you won't get zero ammonia!