LOL I lived there on and off for two years and started going on vacation in the area when I was 15 and I still have lots of friends there. Of course the fact that I LOVE the food, the area and the people there helps too! :)
As far as the train goes, I wouldn't count on upgrading once you are in the train since you might not see the person checking your tickets until late or not at all.
One way to insure that you'll get a seat is to get a ticket AND a reservation. The ticket is good for any train going from Rome to Chiusi that day, however the reservation will reserve you a specific seat in a specific wagon. IMO, it's a great option if you have time to make sure you enter the right wagon at the Termini station in Rome because I've had to hop on a train last second before and walking through tons of wagons to find my assigned seat. No fun! Especially if the train in crowded and people are standing in the hallways. However, you should be fine in September as far as crowd goes but after your long travel, I am sure you would prefer to sit down!
The change in Chiusi shouldn't be a problem, it's a small train station. Make sure you are ready to hop off the train when the train gets into Chiusi, they don't wait around much, then you'll probably have to go down a set of stairs to reach and back up another one to reach the right platform. There should be big poster like sheets (I think white) that have all the train schedules with platform numbers. If you can't find one, run into the main building and they have a big automated board with the platform numbers as well.
Are you in the clear as far as taking the Leonardo Express from FCO to Termini to catch your train to Chiusi?