In order to attach the hardware to the underside of the top half of the stool seat, you need to have an access hole for the mounting screws.
Here is the procedure to make this hole using a router.
Step 1: Determine the hole-position by measuring the distance between the mounting holes.
To set the router up to cut this access hole we will use the same circle jig that we used to cut the outside edge. We need to re-position the center to match 1/2 the diameter or the radius of the mounting screws.