I have looked all through Arizona's website for our Department of Agrigulture and cannot find any requirement for hatching egg importation. I do find (which surprises me as I have previously found no improt requirements) that poultry who are imported must have either a health certificate or the NPIP form you refer to. It is very obvious from the context that they are talking live birds, not eggs.
There are lots of specifics about eggs for human consumption, but none for hatching eggs.
There is no permit required.