I do a similar thing kernelstubbs, but have an additional repeat within the hands empty.
This inner most repeat is an "until Log storage is NOT empty" and causes a loop of nothing. So the robot sits idle waiting for some room in storage before proceeding. The combined repeats mean the robot handles the storage filling up before or after the robot having an axe.
Note I just make a bunch of tools and leave them on the ground near my workers, so let them find their own tool :)
It did take a bit of trial and error to get to this working setup.