Unused lines is inevitable if it's going to be modular, I think, but I take your point. I'm hoping that by painting it cleverly, they'll be subtle. If this project is ever a go-er I'll make a thread about it.
The 12 inch circles should work - if this is a 3 ft x 3 ft board, the hypotenuse of a quarter of it (the diagonal line across the middle above) is root(18^2+18^2)- about 25 inches long, so a 12 inch radius wouldn't quite get up to the halfway mark.