Tom is nearby, but not in Virginia (unless he’s moved). Caveat: I am no lawyer, but have had a lot of vintage cars in Virginia. Title and registration are two separate issues. Value is a third. In order to title a 1968 Jaguar I had bought from Alabama, I used a notarized bill of sale. That was alright because in 1968, titles for car were not mandatory in Alabama, if memory serves correctly. The Virginia could not require a document that did not exist in 1968. I believe the did title cars in Virginia in 1965 era, so this may not be an option for you. But you absolutely need a notarized bill of sale. Imagine a seller finding the old, missing title later on and calling the authorities to accuse a buyer of stealing his or her car, which can be a plausible scenario if proper documentation is not in the buyer’s hands.
BTW, what year is the Tiger? Was the VIN tag ever removed? I ask because the Virginia State Police may want to inspect the car as a part of the retitling process. If the VIN tag was removed, you may run into some problems. This is important with a Tiger because you will end up with a new, State issued VIN attached to the chassis, which can cause problems with the perceived authenticity of the Tiger in the future. I’d be spooked, maybe. "Stories" are never helpful. I had a 1973 Porsche 911 that had been stolen at some point, which had a Virginia state issued VIN plate on it. It was harder to sell the car at the value of other 1973 911s when I decided to. In that case, I think the buyer wanted a race car, so he did not car too much about the VIN issue. Just food for thought