Your AZ permit will not even exempt you from the 180 day residency requirement (which is in section 005.01G) because the exception for the 180 days residency stated in the same section is "Beginning January 1, 2012, if an applicant recently moved to Nebraska and possesses a valid permit to carry a concealed handgun issued by his or her previous state of residence that is recognized by this state pursuant to section 69-2448, such applicant shall be considered a resident of this state for purposes of this section;"
You non-resident AZ permit was not issued by your previous state of residence, so it is no good for that either.