Sounds like you're doing it all well
I also used a MJ with the lid slightly open, and used the airline with the little ball valve to add some air to the tub for gas exchange. Not sure if it made a difference, but I'm sure it didn't hurt
You probably should be testing for phosphates as well
Seeing nitrates drop to zero will give you an indication of when the rock is finished cycling, but you want to see and end to PO4 leaching as well if you don't want any nuisance algae in your DT
Are you using RO water ?
Have you read
Myka's write-up on cooking ?