I'm not familiar with AZ tax rules, but a reading of the form instructions implies that if it qualifies for the federal exclusion (deduction), it qualifies for AZ. And you do qualify for the federal exclusion*, because coming up short of the 2 year rule is due to a job change.
The AZ form starts with the federal AGI (which already excludes the home sale gain). There is no where to add back that exclusion, on the AZ form. I don't think you'll encounter a place in the TurboTax Arizona interview to add that back.
Find form instruction at https://azdor.gov/forms/individual/form-140-arizona-resident-personal-income-tax-booklet
*When you don't meet the two year rule, the maximum exclusion is reduced. In your case, the maximum exclusion is 703 days /730 = 0.963 x $500,000 (Married filing jointly) = $481,500.
