There are companies that do private vehicle registration services. Check your individual State.
When I first bought one of my Mustangs which was also missing the windshield VIN plate, and it was on a Bill of Sale. Totally legit car, but no record for the VIN in the California DMV database. This was around 2006, AAA had already lost the ability to do lost title transfers in the State of California.
Because the Mustang was a stripped rolling shell, I was turned down flat by the DMV. Went through two different managers, trying to plead my case. Their rules state that since my car was incomplete and not roadworthy, they would not give me a license plates, title and registration. I explained that was only looking to get a title, they said come back when the car is roadworthy. I even reminded them, that by their law, I had 15 days from the sale date to notify the DMV. The highest manager agreed that it was contradictory.
I contacted a private registration company. They inspected the VIN, collected my DMV fees and taxes, and filed the paperwork on my behalf. In 2006, my total cost was $55-65, which included a notary fee. Within 3 weeks, I had a title mailed to me from the California DMV.
There has to be private registration companies, that can legitimately secure a 1970 title for that car. I am sure that it is on the owner to do their "do diligence".