A few more times round the inner diameter with the sanding-drum, and...
...dropped.
"
Look Mum, no gap!"...
Much to my surprise, the outer diameter, of the thing or washer, where I had simply and randomly stopped sanding, turned out to be exactly as that of the scope-cap...
That is what is known, in a strange vernacular, as a "coinkydink".
Next, I will need to reduce the outer diameter of the thing until it drops into the cap. It won't take too terribly much to drop it, only the thickness of the wall of the cap there.