What a wonderful plan! Most definitely suggest hitting several on the days out, and enjoying time at your place or nearby on the other days, to make sure you do relax and are not on the go the entire time.
I see Lucca on there near Montalcino and Montepulciano - it is on the opposite side of the region so definitely one to do separately. Have you already been to Florence, since I don't see it on the list? How about Pisa?
You could do something like this, divided by days -- leaving yourself flexibility to do or skip anything as you come to it.
- a whole day dedicated to Siena, adding in a quick stop in Castellina in Chianti on the way there since you're heading down from Panzano. You could add a quick stop to Monteriggioni on the other leg of the trip to Siena, on the way back. But only if it isn't dark yet, I'd suggest doing the drive from Monteriggioni towards Castellina as it is very scenic amongst vineyards. You can do it on another day's drive out as well, when you head to San Gimignano or to Volterra.
- a day dedicated to Chianti and it's towns: Greve, Monterfioralle and Badia a Passignano are all very quite close together so make sense to do at the same time.
- San Gimignano - most don't dedicate enough time here, but I'd suggest adding in a winery visit nearby, lunch and a museum (the Duomo and the Palazzo Civico tower next door are my recommendations), not necessarily in that order.
- Volterra + Colle Val d'Elsa on the way there or on the way back. It is quite small but scenic.
- Val d'Orcia - a whole day at least since you drive down past Siena, take the SS2 through Buonconvento that way you do part of the Crete Senesi, then on to Montalcino, then San Quirico, Pienza and Montepulciano. As you can see, the drive is short but you'll want to stop and even if most of these towns are small, they still do require some time spent there. A drive back through Asciano or Rapolano Terme will ensure you see more of the Crete Senesi. I'd be more for suggesting breaking this part into 2 days, so that you aren't rushed. Do Pienza and Montepulciano separately. The drives in the smaller roads are what scenic Tuscany is all about and you want to stop and enjoy the views too, especially for who is driving ;-).
- Lucca has to be done on its own, unless you want to add in some stops along the way - depends on the route you take.
I could suggest more places to stop at but not sure I want to add more to your wish list and overwhelm you :-D I think the best frame of mind to maintain is that it would be lovely to see everything, but you'll go along and stop where you can and enjoy that!