Did you miss the part in the 2nd Rescue article about not doing water changes for nitrite but rather using the chloride in salt to keep the fish safe with the nitrite present?
Cycling with fish present is a tug of war. You want it to be done ASAP. However, water changes slow a cycle. So they should only be done when absolutely necessary. The 2nd article explained how to know when to change water for ammonia and when not to do so. It also explained why not to do them for nitrite at all unless it rached over 16 ppm on an API kit. Seeing that involves diluted testing. That is the level when it will stall the cycle itself.
It also explained that it take about 24 -48 hours for nitrite to exit a fish once inside and where it is doing harm. As long as there is nitrite in the water it is entering the fish. The chloride in the salt blocks the itrite from entering. This keeps the fish safe.
By allowing the nitrite to bild and remain beecause you block it, the nitrite bacteria will reproduce faster and the nitrite will be handled by the cycle a lt faster. Another way to say this is doing water changes for nitrite does more harm than not doing them and adding the proper amopunt of salt.
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Ichthys
The reason not to detox the ammonia during a cycle is that the bacteria prefer ammonia, aka NH3. Changing it to NH4 (or other form) slows the cycle because the bacteria cannot use it as efficiently. This is why the cycle appears to stall as the pH drops below 7.0.