I think there is something going on here that is slowing the growth of the Nitrospira species of bacteria. These are the ones that are more sensitive to the parameters, and are slow growing. These are the ones that turn NO2 into NO3.
Here is the fishless cycle. Look through it for the optimum parameters for growing these bacteria as fast as possible. See if your tank meets these requirements and keep on feeding the bacteria with ammonia.
Fishless Cycle
Set up tank and equipment.
Fill with water, including dechlor.
Optimum conditions to grow these bacteria the fastest:
GH and KH at least 3 German degrees of hardness, and higher is just fine.
Add some other minerals, for example plant fertilizers: KH2PO4, trace minerals.
High oxygen levels.
Good water movement.
A place to grow. They grow on surfaces, not drifting free in the water. Filter media is great. Sponges, floss, bio-media are all good places for these bacteria.
You can add a starter culture of the right bacteria if you want. It is optional. The cycle can go faster if you add something. Media from a cycled, healthy filter. Bottled bacteria containing Nitrospira species of bacteria. Do not waste money on anything else.
Add ammonia (no surfactants, no perfumes) to test 5 ppm.
Test daily. Add more ammonia to keep the test at 5 ppm through the first few days.
Test for nitrite. When nitrite shows up allow the ammonia to drop to 3 ppm.
Test daily, adding enough ammonia to bring the test to 3 ppm once a day. If you are growing plants that do not like this level of ammonia then test twice a day, and add enough ammonia to bring the test to 1 ppm twice a day.
If the nitrite gets to 5 ppm do a water change. Perhaps add less ammonia for a few days. The nitrite removing bacteria (Nitrospira species) are slower growing, and the ammonia removing bacteria might be making more nitrite than they can deal with.
When the ammonia returns to 0 ppm after 24 hours, and no nitrite shows up at that same 24 hour mark, then the cycle is done.
A fishless cycle with no plants might have VERY high nitrate. Do a BIG water change, or even a couple of them to get the nitrate way down before adding the fish. You can fully stock the tank.
A fishless cycle with lots of plants might show almost no nitrate. The plants are part of the bio filter, and are removing a certain amount of the ammonia before the bacteria even have a chance to turn it into nitrate, and then the plants are removing some or all of the nitrate produced by the bacteria. I would still do a big water change.
If the fish you want to keep need water different than the hard, alkaline water that grow the bacteria so well, now is the time to change that to softer, acidic water. While you were trying to grow the bacteria as fast as possible you wanted optimum conditions for the bacteria. Now that the colony is well established you can change the conditions. They might not grow so fast, but that is OK.