I will toss this into the mix ( from a fellow old timer
) :
If you are getting a nitrate reading, there is obviously bacteria in the tank to convert the nitrite to nitrate. Unless you are have that much nitrate in your source water, you might want to check your test chemicals to confirm they are accurate. ( Nitrate reagents tend to go bad the fastest.
) If you are using test strips, they tend to not be as accurate as liquid reagents.
Next would be when you are testing. Try testing first thing in the morning before adding any food.
"Stalled" cycles are usually due to a lack of bacteria to convert Nitrite to Nitrate. ( Low Ph values would prevent ammonia from being converted into nitrite so the cycle would not have started so it couldn't be "stalled".
) Considering that these do take some time to develop, it's understandable that people think the cycle stalled while in fact, it just hasn't completed it's natural course.
Here's a solution: If you have access to a cycled aquarium, adding some filtering material from that tank or a good squeeze of " dirty" water from an established sponge filter should solve your problem. ( The squeeze system is how I usually cycle tanks in my hatchery.
) The reproduction rate of nitrifying bacteria is quite rapid so there should be no ammonia or nitrite present within 48 hours.
The bottom line is your numbers don't really make sense to me which is why I question the testing materials. As you probably know ( or maybe forgot?) the nitrogen cycle, if drawn on a graph, would look like 2 camel humps. In order for nitrite and ammonia to be present at the same time, the ammonia would need to be on the downward curve while the nitrite would be on the upward curve. To have nitrate and ammonia present together would mean that the nitrate is not coming from the bacteria but more so from the source water. Over the years, the water systems have become much more complicated than in the past. Many water companies use Chloramine ( ammonia combined with chlorine to prevent chlorine evaporation) instead of just chlorine. You need to use something to break the ammonia/chlorine bond ( ie Seachem's PRIME or Kordon's Amquel) before adding any water. They also flush their systems with all kinds of chemicals that they didn't use in the past. Welcome to the new way to fish keeping.
Hope this helps.