I think there are two avenues of investigation that may produce an answer.
1. Look for a commonality in the cast-in part numbers. For example, here is the part number on the vise nut of my 5198 (5V7816S):
Is there a vise manufacturer who used a similar alphanumeric scheme for their part numbers? If as a group we can look at Reed/Columbian/Rock Island/Starrett vises from the late '40s through the late '50s and find one with similar numbers, that would be a big clue. This assumes the part numbers are from the manufacturer and not Craftsman specified.
2. Take a detailed look at the jaw serrations. Whose jaws do they most resemble? I doubt anyone created a new serration process. Most likely Craftsman specified a serrated jaw and left the details to the manufacturer who would have used their standard process. Is there a serration expert in the house?
BTW, my money is on Rock Island.