Good to read the tank upgrade has helped them get more active.
The toxicity of ammonia readings all depends upon the water temperature and its pH, warm alkaline is far more dangerous than cool acidic.
Even if you are running the old filter (or its contents/media) in the new tank, despite being "cycled," you can experience toxin spikes if the old sand/bogwoood etc. do not transfer over too. The beneficial bacteria will grow on many surfaces of a tank, not just inside the filter.