The problem with Bone (I have both Bill Jones Books) is that it's too young these days. In the days of Bone turners it came from old animals and was much stronger, Nowadays our food animals are killed to young for their bone to be good for turning.
I've also turned Tagua Nuts, fantastic things, hard but take a great cut and finish. They used to be used to make buttons (imitation Ivory ones). The trouble is the big void inside them. I'm sure the button turned of yesteryear knew how to cut them to get the best sections from them, but I've never worked it out. So you might go through several to get cut you need to make the pins, you don't say how big they need to be.
I've never turned synthetics, so no advice to offer on them.