You've got it. Just insert the new needle (size 15) and continue on as if it were the other end of the circular. And right again, binding off in purl is like binding off in knit but you'll be purling the sts. You might also find htis video
helpful to avoid a bump on the last bind off stitch.
Post a picture of the bandana cowl if you'd like. It'd be fun to see it.