I bought some stiff irrigation tubing of the correct outside diameter, and some stainless wood screws with heads slightly smaller than that. I put two layers of heat shrink on the top 1/2“ of the screw such that the tubing was a snug fit.
I calculated the distance between the eight post holes, and the distance between 16 post holes. I set up the laser line aligned with the straight lines on the board and stepped at 16-distance from where the laser intersected the centre circle. I then set the calipers to the eight-distance and stepped around the circle. When I got back to the first hole I was about 2mm out. Not too bad. I then drilled out the holes with a 2mm drill bit, in a state of pure terror.