2 1/4" does not leave much leeway. Have you considered sewing the binding down with a basting stitch (machine stitch length set to as long as it goes)? Then you could turn it over and see where you missed. It would be easy enough to adjust in those areas and the basting stitch would be easy to pull out.
I use a decorative stitch when I sew mine on by machine (mostly I sew it down by hand - wearing braces). The decorative stitch gives it another feature and detracts from where things are not perfect.