I know Marti can do the type of research you seek. Yeah, the online forms for Standard, Deluxe, and Elite reports do require the full 11-digit Vin. I have a couple of friends who had a chance to acquire what was pretty much a bare-body shell but wanted to verify it was what some people had told them.
I know Marti went from weeks to months behind during Covid 19 with no staff working in the office. They still have a pre-Covid notice they haven’t updated in a while, stating as of September 15, 2015, they were at the limit of their research capabilities.
As Hemikiller stated, the first two digits are vital as they identify the model year and the assembly plant, while the following six numbers are the numerical sequence of an assembly. Since each Ford assembly plant starts with 100,000, that underlines the importance of having those first two digits. Somewhere out there in this vast land, there is a full-size Ford, Fairlane/Torino/Gran Torino, Pinto, etc., with the same numerical sequence assembly number as what could be on your Mustang.
As you remarked, many of these 50+-year-old cars have been picked clean of ID # bearing parts such as padded dash assembly, driver’s door, engine compartment stickers, and labels. Unfortunately, that also includes the engine and transmission, which had partial Vins.
As suggested, I would continue calling/emailing them. I believe they are still in catch-up mode. I did order a Deluxe Marti report on a project car last month and had it within the week. Even a basic standard report would give you a breakdown of the Vin, standard and optional equipment, and the selling dealer code.
And as midlife mentioned having the full Vin and being able to verify it with the DMV should go a long way in making sure there are no legality problems later on!