How about using a very thin line of washable school glue on the binding to hold it in place while you sew. Try Sharon Shambers method for gluing binding and adjust her method to your machine sewing.
https://www.youtube.com/watch?v=a2hWQ5-ZccE
I think there are two parts to this lesson and this will get you there and I think it can help. She hand stitches her binding and if you glue it after you flip it the binding to the back and press it, it should stay in place.