I think you are on the right track. 40mm Forstner bits are fairly common. A cylindrical 40mm flat-bottomed hole, 20mm deep, will hold your ball exactly as you want it, with no complicated sanding, etc. The fact that it is not a half-round cup hole, will not be visible. If you want the ball to rotate in the hole, so much the better - only one friction point at the bottom of the hole. If you do not want it to rotate, one dab of hot-melt glue at the same location.
Interesting how one gets to overthink situations.