Because the edges of the piece were uneven, and cut so close to the embroidery, I thought I'd do a better job if I turned under the least tiny bit I could, then applique it.
Also, I didn't like how I thought the nap would behave if I tried sewing the velvet on the diagonal.
After basting around the perimeter, I stabilized the vertical edges further with this stitch shown below, which I know has a name that I cannot remember- I wanted those horizontal stitches to fight against the tendency of the fabric to slip along the velvet nap.
After applying self-welt I decided to have a go at sewing front to back with just pins. I wasn't sure if I'd need to baste the seams, too. It took more pins than usual (well, usually I don't use pins at all on pillows) but it sewed up just fine.