Yes, you can use the partial exception. Arizona conforms to the Federal rules. Please see this link for more information. Arizona Sale of Home
You can always call the state directly. The phone number is (602) 255-3381
[Edited 1/18/2021 @ 1:06 PM EST]
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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.