The problem was that you had the food stockpile on priority 3. You only should prioritize something for a short amount, or if its not done consistently. In your savegame they were simply too busy making food to do anything else.
You had your workshops on priority 1, but since their goods were already produced, that didnt matter. You needed a stockpile that takes those goods at a higher priority than 3 (or turn back your food stockpile priority to 5, which is what I did here). The workshop priority is only for producing the goods, not for carrying them into stockpiles from the workshop.
A good example of a continuosly high priority setting would be something that is only being build when you need it. Say for example the carpenter. The dwarf wont build it unless you make planks, which dont spawn "randomly". But as soon as you make planks, your Dwarf will get to making new crafts asap. Putting a high priority on food stockpiling for an unending amount of time is a bit of a bad idea, though
Edit: You dont need to build the extra stockpile of course. That was just for the sake of having a smaller screenshot, heh.
