Things never do go as we hope
Each 1ppm ammonia you add is turned into 2.7ppm nitrite and then on to 3.6ppm nitrate (I think, need to work it out again!).
Going back through the thread, the timescale is:
22 Sept added ~3ppm ammonia23 Sept readings am 4ppm, nit 0
24 Sept - am 4, nit 0
25 Sept - am 1 or 2, nit 0
27 Sept - am 0, nit 0
27 Sept added 3ppm ammonia28 Sept am 0.25 to 0.5, nit 2
29 Sept am 0, nit 0
29 Sept added 3ppm ammonia29 Sept (after 12 hours) am 2 to 4, nit 1 to 2
30 Sept (just under 24 hours after adding ammonia) am 0.5, nit over 5.
What I am thinking is:
You had some ammonia eaters and nitrite eaters survive since the tank last had fish. But we didn't know how many of each you had. It took the ammonia eaters 5 days to deal with the first ammonia addition, 2 days to deal with the second and about 1 day to deal with the third. Because they made nitrite slowly, there were enough nitrite eaters to deal with this trickle as it was being made after the first addition. But nitrite eaters reproduce less quickly than ammonia eaters. As the ammonia eaters multiplied they made nitrite quicker than the nitrite eaters could keep up with. You are now at the stage where you have virtually a full colony of ammonia eaters but not nitrite eaters; you need to wait till they catch up. And because 1ppm ammonia makes 2.7ppm nitrite, the nitrite reading shoots up quickly once it starts to build.
Can I ask you to do a diluted nitrite test. Try 50:50 tank and tap to start. If the reading is still off the top of the scale, try 25:75 tank:tap. Once you have a nitrite reading somewhere on the scale, multiply it by whichever dilution factor gave that reading to find the actual level in the tank.
The problem we have is that our test kits for nitrite don't measure high enough. The critical value is 15ppm. That's when the nitrite eaters become inhibited. If your actual level is below that 15ppm, leave the tank alone. If it is above that, do a 50% water change.
But don't add any more ammonia till I know high high the nitrite actually is in the tank.