You've prioritized what you want to see, which is great. Haven't been to Venice, so I can't help much there other than to say your 3pm lunch plan is may involve panini or pizza in a cafe, as full-serve restaurants tend to close from about 3pm-7pm.
Florence: The Uffizi IS closed Mondays, so watch out for that in your timing. I'd still drop Pisa unless you just have your hearts set on it. Fiesole and even Lucca are closer, and you haven't left much space if things go wrong (trains are frequently late, your feet hurt, you have to drop off your shopping bags, etc.)
You didn't detail out Rome, but we had 3 nights (Tues, Weds, Thurs nights--left Fri) and what we did was the following:
Day 1: arrived, visited Santa Maria Vittoria, did Rick's Night Walk in reverse from Spanish Steps to Campo de Fiori, dinner.
Day 2: Colosseum, Palentine Hill, Forum. This took about til 2 or 3pm, grabbed a quick bite, then went to the Borghese Gallery for a 5pm reservation.
Day 3: Vatican & St. Peters, also climbed the dome. Finished about 4 or 5pm, and walked over to Trastevere to see the church and just wander around.
We also squeezed Trajan's Forum and St. Peters in Chains into our last morning there, as they were both fairly close to our hotel. Also, this was in November when it's easier to get around with less crowds, so you may not be able to cover as much ground.
Hope this helps your planning!