The hat is also a moss stitch with a rib stitch rim. The ribbing gives it a more grip so it still has some extra stretch to it that helps it stay in place without sacrificing comfort.
I had changed how I do this one from the original design to minimize the number of pieces and seams there are. The stockinette portion for the body is all one piece instead of the three it was originally designed as. The sleeves are attached on a raglan stitch to add a bit more detail along the diagonal. I also added a single crochet border to help it lay flat. It still has plenty of stretch, but stockinette stitches tend to curl, so the trim helps to eliminate the curling similar to a patterned stitch.
The only thing missing now are the buttons! I'm very close to having this commission wrapped up before moving into a few other baby knits, a baby knit revision, and some shark mittens!