John,
My suggestion would be a more logical route, similar to the one that Judy suggested. The Itinerary you've proposed is very inefficient and involves a fair amount of "backtracking". Your trip appears to be about 14 days and with such a short trip, an efficient and logical travel route is essential!
My suggestion would be along these lines:
Jun. 27-Su: Depart U.S.
Jun. 28-Mo: Arrive Venice / VCE (use Alilaguna Water Bus to Venice?)
Jun. 29/30-Tu/We: Tour Venice (you'll have to pace yourselves, as you'll be jet lagged)
Jul. 1/2-Th/Fr: Train to Florence; Touring Florence (reservations for Uffizi & Accademia would be a REALLY good idea if you plan to visit there)
Jul. 3-Su: Train to C.T. via Pisa (you can determine the train details later but allow at least 2-3 hours if you're seeing the Tower); continue to Vernazza; arrive ~14:30.
Jul. 4/5/6-Mo/Tu/We: Tour Cinque Terre
Jul. 7-Th: Depart ~07:15 for Siena via Pisa & Empoli, arrive ~14:15 (3 changes, reservations compulsory on one section). Taking a Taxi from the station to the city (which is on a hill) is the quickest method.
Jul. 8-Fr: Tour Siena
Jul. 9-Sa: Train to Rome. This will be a full day! I found one train departing ~07:30, arriving Roma Termini at 15:58 (time 8H:26M, one change, reservations compulsory). This train has a layover in Pisa, so you might fit the visit to Pisa in here instead.
Jul. 10/11/12-Su/Mo/Tu: Tour Rome. Plan your touring carefully and pace yourselves as there's LOTS to see. Packing a copy of the Italy 2010 Guidebook would be a good idea as it's great for reference.
Jul. 13-We: Flight home (use Leonardo Express from Termini to FCO - €11 PP)
This Itinerary would fit all the places that you had on your list, but of course you'll have to adjust it to fit your time frame. This is a bit of a "blitz" so you could drop one place to provide a more relaxing trip.
Congratulations and happy travels!