Hi, Kevin,
You seem to have gotten a few different ideas but, in my honest opinion, I think all you
really have to do is slow your scroll saw speed down, then slow your feed rate down accordingly
and just follow the line of your circle to get the 1/4" or so lip that you like around your finished piece.
Since you asked, I will state that I do not care too much for the square backer for a round clock.
God Bless! Spirithorse