So the strokes are just lines?
Select the lines, then go to Object > Expand. This converts the lines into shapes. If the lines overlap eachother, select them all and combine then into a single shape by clicking Unite on the Pathfinder palette. Then select this shape and punch it out of the circle using the Pathfinder palette again or your method of making a compound path.
I hope that helps.
A compound path is not limited to two subpaths. See online help about Compound Paths, Path Direction, and Winding Rule.