When driving into Rome, it's critical to know the ZTL active times. For the city center they're M-F 6:30 AM to 6:30 PM, and Saturday 2:00 PM - 6:00 PM (the ZTL is NOT active in Rome's center on Sunday's or holidays). On Friday and Saturday evenings, some ZTL areas (including the center) have an 11:00 PM to 3:00 AM restriction, so get yourself a good map to know where those active ZTL areas are.
You may want to adjust your arrival time by an hour if you'll travel through a ZTL restricted area so you don't run afoul of the open time driving a car is allowed, targeting an arrival time of 7:00 PM so you don't enter the ZTL before 6:30 PM.
Regarding your proposed route - the drive time itself is 4-hours 45-minutes, if you switch Montepulciano as first stop, then Pienza, you're still driving 4-hours 39-minutes, so no real time savings, but your route (IMO) is a nicer drive. I'm not sure I'd try to make three stops to explore in one day with that many hours of driving along the way (and we road-trip a lot) - is there a reason for the towns you've chosen? Are there things you specifically want to see, or just poking around? If you opt to do just one, like Civita di Bagnoregio, your total drive time is then 3-hours 40-minutes, which would give you one more hour off the road to explore.