David, some outboard motors had shear pins, as you probably know. A newer concept is rubber lining the inside of the prop so that the rubber will serve as a slip clutch. Theoretically, the prop will spin on the prop shaft if the prop hits a stump or a rock or a floating body or something. LOL The problem is that the rubber can deteriorate over time. It can get very hard as well as move around. That may be the reason that it doesn't fit the shaft. Since you have contacted the manufacturer, you might check with them again to see if this has been an issue and you can use the prop nut to help force the prop onto the shaft.
I had a Sears 5 horse motor that I believe had the name GameFisher on it. Came on a used 16 foot aluminum boat and the whole deal was less than a grand when I bought it. You might check also with your friends at Sears to see if they have the manual and any parts for a "comparable".