Mr. Mark:
Rules - each state has their own set of title/registration/and inspection rules. CA likely the toughest.
My foreign "import project" was not vintage, or historic (again, different states, different definitions) at the time.
And yes, some states offer Vintage registration. My Indians (all pre-'47) and 1960 R69S have Vintage plates (registration), good forever. But they started as USA titled vehicles, and no rule how often/when they can be driven on public highways. Not AZ or CA, so different state, different rules.
One other "wrinkle" I forgot to mention earlier was the tax - import tax to Uncle Sam, and then there was a gray area about a state tax. Both were based on original price in some government Department of Transportation book.
Your other option posted was Arizona. I'm a member of the SEAT Club of AZ, (BMW club). One member got in a John Player Norton, but it's possible he did it when he was in the Army (lot's of military in AZ, nearest me was an Army base). I can't remember how or when. Send me a PM with a private email and I'll ask him if he wants to share facts.
Sidebar: I met a fellow in CA who had spent the big $'s to ship (by slow boat) a cheap ($200-$300) Minsk to the USA from Vietnam. Don't know where it came in through US customs, but he carried it around in the back of a truck, off-loaded at events, like the HU Meeting. When I asked him about the "How?" and "How much" his answer was "Too much!" and why could not drive it on the public roads. Plus, it being an old smoking two-stroke, I suspect it would not pass CA emissions.
If your AZ based '83 is not on overstay in The Great Computer In The Sky for the USA, you might want to exit to Mexico, and then re-enter.
I've also seen, as you noted, foreign imports with USA titles/tags (several I know came in from Japan), so it can be done, but where, how much and how long is murky. Sorry I can't be more specific other than to say I know it can be done, 'it's the "How" and "How much" time and $'s that are gray.
Best,
Dr. G
Chief, World Adventure Affairs Desk, CITY BIKE Magazine
Survivor:
www.greataroundtheworldmotorcycleadventurerally.co m