I would apply tissue paper over the background area containing the unwanted overspray, then sew and quilt as usual. Remove most of the tissue before washing. Remaining tissue paper and all basting spray will come out in the wash. At worst might need to tweeze a few paper fragments from stitching lines after washing. Or, more expensive, use a wash away stabilizer instead of tissue paper. All that is needed is to cover up the stickiness of the spray until the quilt is washed.