If nitrites are not being converted to nitrates, wait it out. Try not to dose more than 2ppm ammonia and give it some time. You're close!
Does your tap water show nitrates?
I would do a large water change or two, re-measure, dose the amount of ammonia it takes to get you to 1-2ppm, then see if it converts straight to nitrates.
The last time I did a fish-less cycle by adding ammonia was 5-6yrs ago. Now all I do is swap a used filter over to a brand new setup and it's good to go, producing nothing but nitrates.