I have come to the conclusion that I don’t have the right tools and workspace for precision engineering but, nonetheless, I managed to cobble together a mounting board (or “dish”) for my Pi.
The Raspberry Pi (with additional LedBorg LED board sitting on top of the GPIO pins) has had a couple of tiny bolts fastened through the pre-drilled holes, which are then pushed into a couple of thin dowels. I drilled small holes in the end of each dowel and hammered the other end into holes drilled in the mounting block. The larger dowels are glued in place on the wood and simply act to provide additional support round the edges of the Pi.
Not incredibly elegant but it will do for now. The next step will probably be to add a clear covering over the top to keep dust off.