However, the timber camps only have sawmills (in the demo) competing for its output, and it doesn't much matter where lumber ends up (except for lumber fetched to go to the boat yard).
I just realized that the cannon foundry will only use lumber from the timber camps and not from the sawmill. Thought I'd chime in with that info. Later on in the game when you are looking to build up your weapons, it looks like the competition for the lumber would increase with more and more cannon foundries. Just a thought.