I purchased a side cutter made by Brother to use on a Brother NX450Q. It did not work well and I returned it. I found others have had the same experience with the side cutter, it does not work well for most applications.
I think you're stating that you currently zigzag the edges of the quilt before applying the binding. Instead of zigzagging, you could straight stitch sew, 1/8 inches from the edge of the quilt.