Just to be sure, do you plan to walk to a restaurant from your sleep, or are you going to use a Agriturismo? What month and year (crowding and heat issues)? Are you going to Siena more than once? Does that list include towns that are must-sees for you, or did you just select likely hotel towns?

We stayed in a rural hotel for ease of parking and avoiding ZTLs. Don't underestimate driving time on twisting, narrow roads for your daily daytrips. I would not change hotels without a 3 or 4 night continuous stay, but otherwise I'd stay in a central location to my visit list. I don't consider Cortona to be near Siena. Google Maps says its an hour, and you have to add 10%-20% to that, more in the summer. Siena has some big peripheral parking lots, but many of these towns require waiting for a space to open up. (But, you do need a car for Tuscany.)

We have used San Gimignano as a base for exploring. We stayed inside the walls which was a nice experience, but not necessary. It also meant finding parking (free) was a bit of a challenge when coming back at night.

Being based in any town allows you to experience it differently once the large crowds leave. We also stayed outside of San Gimignano in a nice hotel. The challenge the was driving was necessary if you wanted to not eat at the hotel.

If you have a car and are willing to drive, chose any town, even one that is not well known as a base. I guarantee you will find interesting sites and great food and best of all virtually no other tourists.

When travelling we often stopped at “no name” towns and had a great meal and interesting tourist sites. Remember guide books all seem to focus on the same towns. Explore and you will find great churches to explore, Roman ruins etc.

Have fun.

1. The area you are planning to visit isn’t great for getting around by train.

I’m wondering if you understand the geography of Civita. It is reachable only by a pedestrian bridge, which, as I recall, takes about 15 minutes to negotiate. Additionally, there are hardly any amenities. Cross it off your list. It would make an extremely unsuitable base.
We once stayed near Chiusi and were easily able to do many day trips because of its proximity to the A1. The drive from our rental to the autostrade was flat, another plus. If you do rent a car, be careful in selecting a town and in choosing lodgings. The hilly, winding, twisty roads cause short distances to need a long time to cover. Also, know what the parking facilities are before you reserve. You will need a place with its own parking or a town with public parking, preferably the former.

Two bases sounds like a good idea.

Last summer I did 2 nights in Volterra, 2 nights in Siena and 2 nights in Montepulciano. I really enjoyed all three towns. As other posters have mentioned, you have to be very specific in your housing search to make sure it either comes with a parking space, or that there is street parking or a parking lot/garage nearby. I agree that Civita does not make a good base. I would definitely visit it, but once you've seen the town, there's not a whole lot to do there and it's a bit out of the way when trying to get to other places to visit. Cortona is also not the most ideal, IMO. It's mostly all uphill and not near other towns. I definitely thought Volterra and Montepulciano were the most atmospheric of the towns you've listed. San Gimignano is also a good option.