I usually use binging also. For turning smal projects, I make sure the seam alliances are at 1/4 inch ( or if circles, I trim with linking shears) On squares, I cut off the corner points down to 1/8.
I usually machine sew across the open spot attaching the one side of the fabric to the quilt batt or insulbrite before turning. If you keep the stitching line a little under the 1/4 seam allowance it will be inside and not seen after turning. This makes it so the insulbrite turns under well for closing.