I didn't see anywhere a mention of your fire. Is it lit? Do you keep it lit at ALL times? That will not only help your research go faster, it helps keep your villagers stay healthy as well.

As stated above, the restorative stew will help your villagers recover. Make the stew, drop ALL your villagers on it before it goes away and their bar will be filled back to full. This is a lot faster then repeatedly dropping villagers on the food cart.