Another option would be to do the circular scoring using a radius arm. A long, thin piece of wood screwed in at the centre of the circle, with a sharp nail driven into the wood at the appropriate point, could trace the scribe mark.
Then, if you have access to an (scrolling) electric jig saw, you could anchor the jigsaw on a radius arm and scroll around the scored line?
This assumes you don't mind having a hole at the "centre" of the work piece where the radius arm would be screwed into.
Cheers
Dennis
PS - as always, test your chosen approach on a piece of scrap wood first!
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