Your experience should be relatively uncrowded in February. I would expect the Agriturismo experience to be, maybe, a little dull at that time of year. There are an unlimited number of hill towns you could visit, but you should understand that they are all "ready for tourism". I'm not slamming them, I'm just telling you that they each have walk-in local produce stores that are an urban dose of agri-tourism. But they have something in common with Zabars. (A New York City delicatessen.)
We liked Orvieto very much, and it is, perhaps, less intensely touristed than Siena. But Siena is much, much larger. Do not rent the car before you use the search box here to learn about IDP, ZTL, insurance, and parking.
Your use of the term "home base for 5 nights" is a little confusing. I can't recommend driving into Florence for your two days of visiting there. As noted, it is a good place to sleep if you are content with the several places you can get to easily by train or bus. But that would be less of a "countryside" visit that you say you want. We didn't stay in an agriturismo, but it seems like you would be well advised to select yours carefully, with a lot of reliable research. Note that the best wineries want an appointment. Mom and pop places, not so much.
I trust that Feb 21 is your arrival day in Florence, not your departure day from the USA. Taking your preferences at face value, I would add a day in Venice (because it is so unique, and because you'll be jet-lagged) and subtract a day from Florence (because you aren't that interested in History of Art, and Tuscan countryside is important to you.)
