Ran into the same issues with our Z when I brought it out of hibernation after 30+ years. Arizona purges the vin after 10 years if not registered. The last AZ plate on the car was from 1987.
I had to actually pay extra fees to recreate the car, and then they took an extra 2-3 days to research it and make sure it wasn't stolen and that there weren't any leans on it. I always wondered how they did that if the vin supposedly didn't exist anymore. Leads me to believe there is in fact some record of the car somewhere, but getting the DMV here to provide any more information on it was like pulling teeth. Turns out the serial number is one of the group missing from the NCRS information too so that was a dead end for me. I gave up.
I basically have a 69 Z that has begun a new life
Hope you have better luck.