What time of year is this trip going to be?
I have to agree that you are planning too many side trips for such a short trip. I commend you for not trying to stay in too many places but trying to take too many day trips can have the same effect of making the trip all about transportation and not enjoying.
I like the general plan but remember that 3 nights is only two full days on the ground so even with 4 nights/3 days in Florence the city deserves 2 days and then maybe a day trip. Pisa and Lucca make a nice loop by train from Florence. You could also do Bologna as a day trip from Florence but you seem to be concentrating on small towns instead which is fine.
Viareggio is really just a very blue collar beach resort town with the usual distractions and I'm not sure I would spend a day of a short trip going there unless you really want to see a beach.
Siena is beautiful, if very touristy, and deserves at least a day one it's own. San Gimignano and Volterra would make a good - if long - day trip from there but you'll need someone else to work out the transportation to do both in one day. The Pienza/Montepuliciano area is at least an hour and half away and is on the very edge of what I would consider enjoyable as a day trip and I would work to visit something closer instead.
The cities you're staying in have their own charms so don't forget to explore them rather than planning to just use them to see other things. I know these things seem completely reasonable on paper sitting at home with a long list of places you want to see but part of it is enjoying the places you've travelled to see. Especially in rural Tuscany part of the experience is slowing down to experience the lifestyle that depends more on season and weather than the hour of the day. As tourists it's hard but remember to leave some time to breathe. I think something as simple as a languid spritz (or two) in Siena's el Campo as dusk falls across the piazza is one of Italy's real experiences. And if suddenly a contrada based flag throwing and marching band procession breaks out while you're there that's a real Sienese evening.
Lastly what time do you fly out of Venice? Early morning flights out of Venice can be tough so I would suggest cutting out the vaporetto and staying within walking distance to Piazza Roma so you can head directly to bus/taxi to get to the airport if your flight is early.
Hope that helps, have a great trip!
=Tod