I don't know much about the Minnesota E. I do know that Sears had their own model numbers for each item. The machine, and the cabinet will have a sears model number on it. You've seen that. The digits before the dot are the actual manufacturers code. The numbers after the dot are the actual model number.
You probably knew that.
In this case I believe the 117 prefix indicates they were made by White. My old Kenmore from the 30s has a 117 prefix and it is a White machine.
I love that cabinet, and am fond of the crinkle paint machines too.
Joe