Thank you, Martin. I will look into your suggestions.
Thank you also, Emily. The only 29 euro fare I saw between Vienna and Venice had stops and a change to bus in Villach. With all our luggage, I think it would be too much of a hassle. We'd also need transportation from the bus station to our hotel. Then we are on to Cortona, so we'd definitely want a car.
Oddly, renting a car from Vienna airport and returning it to Florence airport is only $400 more than renting it in Venice for fewer days and returning it to Florence.
It looks like the best option will be to rent a car in Vienna, stop around Graz for the night, and then continue on to Venice.
Any suggestions on hotels and/or restaurants along the way?
Thank you for taking the time to help a stranger!