If I understand what you are trying to do correctly (my machining background) it seems that you could make your own tool. While crude it might be sufficient.
I gather it has to be pretty small. Can you find some small steel, stainless steel tubing, spacer, etc that has an outside diameter that is the desired size of the 'spot'. File, with a jeweler's file, two, three or 4 teeth. What you are machining is soft so I don't think shape is too critical.
To center the tool insert a pin - made from a broken drill bit, piano wire, etc - that is small enough to fit into the hole in the board and the tube/spacer. Epoxy, solder or braze in place. Won't be perfect but it might work.
An alternative is to grind the end of a drill bit down, that is the size of the desired spot face, so that the end becomes the pilot. On a large scale that's doable - quite the challenge at this size unless you know someone with a mini-lathe.