The thing to realize is what is in the bottle of bacteria you added. It is both ammonia and nitrite bacteria. And they are there in the proper balance. This means whatever ammonia is handled, there are enough nitrite backs to reals with that.
The bacteria in the bottle are basically dormant. They are that way because in the bottle they lack what they need to fundction as a group- ammonia, oxygen and inorganic carbon. They are in good shape but asleep. When you put them into the water, they wake up. They have to find a nice place to settle on and then they go to work.
Next, Dr, Tim is a scientist. He works with the nitrogen scale. R=that is why the instructions say: " Day 1 – dose ammonia to 2 ppm ammonia-nitrogen [NH3-N] " That -N lets one know this. If you have the right kind of test kit, you might be able to read the NH3. But most kits use the total ion scale. However, it is possible to convert between the two. If you added 4 drops/gallon you will not get 2 ppm, you will get between 2.4 and 2.7 ppm (2.56 target). The factor I use is x 1.28. So 1 ppm NH3-N = 1.28 ppm NH3.
The same thing happens with Nitrite only the number gets bigger. Dr. Tims's 1 ppm of nitrite on hobby test kits = 2.55 ppm.
I am going to guess you are using API test kits. If so you need to convert the numbers in Dr. Tim's Instructions.
For ammonia multiply them by 1.28
For nitrite multiply them by 2.55.
Wait to add another 4 drops/gallon when ammonia is under 1.28 ppm.
Also, please answer the following ( I caould not got back and read the whole thread, so forgive me if I ask something you arlready posted)
You shook up he bottle of bacteria before you added it?
What brand of dechlor do you use? If you have one that binds ammonia, this slows the cycle and also messes with ammonia results.
How long after the big water change did you add the ammonium chloride and bacteria?
What were your test results for ammonia and nitrite on day 2?
Does the tank have substrate? If not this can also slow the cycle.
Are there live plants in the tank?
What filtration aeration is on/in the tank?
One last observation. You are trying to establish microscopic organisms in your tank. You cannot see them and you cannot count them. The only way you know you have them is your test kits. Testing and keeping a record of results is important when cycling. This is because cycling is a process. It has to follow a specific order. There are factor that can alter the speed of a cycle and even stall it. And the only way to know what is going on in such cases is testing. Also know what can throw test results off is important to know.