I would cut back Siena to 2 nights, pick up a Hertz rental at the train station, spend 3 nights in the countryside [perhaps Montepulciano]:
We arrange our cars by calling up the broker Autoeurope [having the use of a toll feee number]; get zero- deductible collision, which covers any damage to the body of the vehicle. Read this about driving in Italy and restrictions involved [ZTLs]; never leave anything of value in a vehicle when parked:
Train Chiusi to Napoli Centrale, quote to be driven to the AC town of your choice:
Regarding Orvieto, Autoeurope stopped using Hertz because of complaints; however train time from Chiusi is 29 minutes. Tickets from the tabacchi in the station for the buses and funicular. The latter does not go all the way up to town [but to Piazza Cahen]. Here are the buses:
Bus 1: Railway Station to Piazza della Repubblica.
Bus A: Piazza Cahen to Piazza del Duomo.
Bus B: Piazza Cahen to Piazza della Repubblica.
Cortona [Camucia-Cortona station] a nice day trip. Fixed taxi fare from the station up to the Piazza de la Repubblica is €12.