If you can qualify for a mortgage on the home in ND as a second home, this could work. You would have to continue paying on the home in AZ until you get the mortgage and close on the home in ND.
Once you short sale a home, you cannot get another mortgage for minimum 2 years if it is FHA and longer for conventional mortgage.
This is called a strategic default.
Contact a CDPE or other experienced short sale specialist in your area to discuss your options and talk to your lender. Keeping in touch with your lender and working with them is a very important part to getting your short sale processed in a timely fashion.
i wish you luck and congratulations on your new adventure!
With regards to your Question I work for a National Lender and based on your situation you would most likely meet the acid tests. Job ouside of current area and current over last 12 months on your current mortgage.
FHA will be the best program if you meet other standard FHA Guidelines.