Foley & Williams made a machine for Sears branded as the Minnesota. It's basically a Goodrich High Arm.
The top tension is not quite the same, but the base and location of the stitch length and the location and type of bobbin winder look more F&W than National. They are two very similar machines like this, probably had some of the same people working on them, and sometimes they were made at the same plant too.
I'd never use something like an inspection plate to tell for sure what the machine is - I've seen way too many machines missing them, and the people will put on what they find available. And it could have happened 60 years ago, when the machine would have still been considered "vintage".
Also - often times the underside is the key to figuring things out. Companies often copied exterior designs that weren't patented.
I've got a National made machine that looks just like a New Home, which is very distinctive. In fact, it does not look like any of the other National machines. The underside is very different from a New Home though.