Not a huge fan of clay recon, but the profile shots on Doenet of the clay and drawn recon shows that this Doe had quite a distinctive nose. I've just finished watching MASH all the way through, and it reminds me a bit of Jamie Farr's. He had black hair, too. If the recons are accurate, it should be easy to rule out missing with petite or button noses. Both the artists seem to have focussed in on it as the distinctive feature and possibly exaggerated it a bit, as I have heard some teachers of recon art tell their students to do.
I'm assuming they have DNA since this is a recent case, and probably dentals. They won't have fingerprints if he was skeletonised. I'm surprised they have hair, but I'm assuming he was put in the bag at or around time of death, so it stayed with the remains after it loosened from the scalp. I assume he was dumped soon after and laid there until he was found. If he'd been kept somewhere and moved in the bag after he'd skeletonised, I wouldn't imagine he would have remained articulated enough to tell where the bindings were or if they were on the body at all. But if he laid undiscovered, they would have stayed in place.
