Axes have a Woodsman's Axe, saws need some love too!
Add a Carpenter's Saw. It produces more boards and does it faster than a Metal Saw, while using less stamina.
Should take something like 1-2 bars of steel and a block of wood, maybe a leather/hardened leather or bone glue too.
Also, the Woodsman's Axe should give more blocks of wood than a Metal Axe.