I don't know how bad the frays are or what kind of machine you have, but most newer machines have a wide variety of fancy stitches. What if you treated the star parts as if you were doing a crazy quilt. You could use a wide variety of stitches, carefully selected to be fairly wide and dense so that all the edges would be covered. Personally, this seems to be easier, less fussy, to do than to cut out alternate pieces and try to get them to match the original. This way, you'd keep the original fabric and "feel" of the quilt; you'd be reinforcing all the seams so that less damage would continue to happen; and you'd be putting your personality into the repairs. I'd personally use fairly bright colors to make the repairs a highlight rather than an oh-oh.