That's a good question about the water change in response to a stalled cycle. I've often wondered that myself. For a refresher, how long ago did you start this?
The nitrite might be off the charts actually. If you dilute it 1:1, 1:2, and 1:4 with DI water, you might get the same dark purple result. Water changes will reduce the amount of nitrite so that when conversion starts, you will see the changes. For instance, let's say that the nitrite is more like 15 and over time the BB reduce it to 10. Both readings are beyond the charts range so you will only see 5+ and think that there is no progress. If you do a water change, it will bring down the levels and you might be able to see a reduction in nitrite and increase in nitrate through testing.
There is no need to add more ammonia unless it drops to below 1 ppm. Adding more won't speed up the cycle.
The nitrite-to-nitrate conversion can be painfully slow. We are talking several weeks or more. If I am reading the results correctly, the first pic has about 40 ppm nitrate and the second about 5 ppm nitrate. Is the first pic from the day before and the second today?