You're almost there! Keep dosing with ammonia (only to about 2-3ppm now), monitor and WAIT for the nitrites to start to drop......(this can be a frustrating wait... I know!). Personally, I've done a 40% water change BEFORE my nitrites were at zero, and they just continued to linger at the low levels for a while after I added fish. I had to maintain water changes to keep them low until they dissapeared.
Officially, when the 2-3ppm of ammonia dissapears in 24 hours....... Your nitrites should be low and getting lower..... Big water change to dump the built up nitrates, and yer good-to-go..... full-on stocking.
Remember, stem plants can take up alot of nitrates from the water column...... if your lights are ok, add some plants..... Fish love live plants!
High nitrates (in the order of >10ppm can cause a bacterial bloom or algae bloom in your tank) Keep the lighting period low to minimize this. I try to keep my nitrates below 10ppm but it depends on the stocking you have in your tank (including plants).
Keep the faith........ patience! Wait for the 'big' move in nitrites.