The KH could be an issue - what is the tank pH now? All the nitrite made during cycling is acidic and when KH is low it gets used up quickly leaving nothing to stabilise pH which then crashes off the bottom of the tester chart. The bacteria we are trying to grow don't multiply at low pH so the cycle stalls.
Plants take up ammonia and they do so faster than the bacteria. When there are a lot of plants, very few bacteria grow because the plants take up all the ammonia. With a few slow growing plants, they can't remove all the ammonia so some bacteria do grow, just less than a tank with no live plants. I think your tank falls into the second type as I can see mainly java fern and anubias which are slow growers.
Few plants take up nitrite, so bacteria have to deal with that. It may be that you have some ammonia eating bacteria and they and the plants are removing all the ammonia; the ammonia processed by the bacteria is turned into nitrite but the ammonia processed by the plants is not. This would explain why you have less nitrite than usual.
The water lettuce plants you have added remove ammonia; they 'remove' nitrate by stopping it being made. Once the water lettuce begins to grow - the plants get bigger and new ones develop - you'll probably find all the ammonia is removed by the plants. Floating plants are particularly good at taking up ammonia because two of their other requirements - light and CO2 - are plentiful at the water surface.
I think you are now at the waiting stage. Waiting for enough nitrite eating bacteria to grow to remove any that is made, and waiting for the water lettuce to get bigger/start growing new plants.