We are kind of waiting to hear from Jim how thick the stock is out there around 12.5 inches. He will need to carve out a 1/2 deep hole about 3/4 wide and about 9/16 lengthwise under the barrel.
Dick, how thick would the stock need to be so a 1/2 round escutcheon would not pull through the stock when the barrel band is tightened? Maybe 1/4 inch? From the photo I am not sure he had that much, that is why I thought of the elongated escutcheon.
You will have a lot more experience that me on how to do stock work without machine tools. I am thinking out loud here, I could take short piece of steel the size of the barrel and drill a precisely square and centered hole though it. This bar could be clamped into the stock fore end and after lining it up, the 3/16 or 1/4  hole could be drilled the stock. The rectangular hole under the barrel fudged out with a Dremel and burr bits.
Not sure if a piloted 1/2 drill could be found commercially or if it would have to be fabricated. Careful use of a hand drill or drill press could do the inset for the escutcheon. I like that word I wanted to call it a washer, ferrule or something else. Now I need to learn how to pronounce it and spell it without copying and pasting.
I have a bunch of steel bar ends, making a oversize  escutcheon to fit the hole with a tight hole for the screw can be done in minutes. Since Jim has time maybe with others input we can figure out how to do this easily.
Those saddle rings on carbine stock, I know the SA would have done them with a dedicated machine how would a stock maker do it without a milling machine?