I machine stitch mine on similar to Cari-in-Oly. I haven't worked with Minky so don't know if this will work because that product seems to be thicker than a normal quilt.
I cut my binding 2 1/2", fold it in half and sew it on the back as a 1/4" seam. When I roll it to the front, I barely cover the stitch line, pulling the extra to the back so that I am stitching on the binding on both the front & back at the same time. Similar to Cari, I sew a few inches, stop and get everything matched up again. For the corners, I've tried two different methods...
1. fold and sew a HST in the corner so that it creates a cap that fits the corner when pulled to the front. The trick is only sewing the half that will be on the front. It's tricky
2. The second way is to fold the corners as you would when hand-stitching and pin securely, then very slowly sew over the pins. I then come back and hand stitch the corners so they don't come apart.