Increase the value of the Sturdy Saw by adding rare drops to the Sawmill. Rare drops would behave like the quarry, where you occasionally get Unpolished Jade and other items. Without the Sturdy Saw, the Sawmill could rarely drop Forest items like Arrowheads and Bird Eggs. With the Sturdy Saw, Sawmill could also start finding Raptor Eggs, Claws, and other Whispering Creek items.
Sturdy Saw is generally considered a weak reward for a difficult quest chain. Even 1-3 free raptor drops a week would increase it's value significantly.
It also makes sense that other items would occasionally come in with a batch of fresh timber.