If your trip is to last 20 days and you spend 3 weeks in Switzerland as you state, how much time do you plan for Italy? Your plans for Italy are sort of exagerated! The minimum needed for Venice is three days, another three for Florence and five for Rome. Add travel to that, visits to the Amalfi Coast, Cinque terre, the lakes, the Dolomiti etc., and you see that it can't be done in a reasonable way: You'll be rushing from place to place, and you'll fly back to the States in a dire need for vacation. And all of this mostly in August where the cities may be empty of locals (several stores and restaurants closed) and the other places you want to see simply innundated by hordes of tourists. Although it may be too late for this (you wrote you've already planned everything), I'd urge you to scratch 50% of your targets and visit the rest in a more comfortable way.

PS Check the Italy forum. Lots of threads concerning visits like the one you're planning...