Holy crap! You're actually considering spending $1,400 for a driver? I want to travel with you!
I'd go for the train or rental car just from a cost perspective, and would likely settle on the train. At least you could enjoy a few glasses of wine or get a little sleep on the train and not run the risk of getting ticketed for speeding or ending up in a ditch.
If you do hire a car, don't get one from the hotel. I've found their prices to be up to double what a private service will quote you directly.
Enjoy Lucca and please report back on the concert...with pictures if possible. Sounds great to me!