Hi Joe -
Oof. She probably won't like this but is she willing to give up Venice or Florence to make this happen? 3 major Italian cities in 8.5 days - and that's not including the three 1/2 days you'll eat up transferring cities/hotels - is sort of pushing it to begin with, and I've the feeling you haven't given Florence nearly the amount of time it deserves. Maybe I'm reading it wrong but it looks like only 1 day?
So my 2-cents? Given the time it takes to get to Positano or Amalfi + enough left to to explore the region, it isn't worth the effort if you can't give it at least 3 nights/2 full days. And the transfer time to-and-from the region will eat even MORE time in transport than you are already munching on.
Aside from trying to squeeze in the A.C, I would consider going directly to Florence on arrival day, then to Venice and then end your trip in Rome. As arrival day is usually lost to jet lag and acclimation anyway, might as well use the remaining .5 day as travel time?
Sample itinerary below. You could swap out a day of Florence for an extra in Venice but Florence is a great base for a number of day trips. While I almost never recommend this, you could consider a day trip the Cinque Terre from there to see some wonderful blue water, weather permitting? You could also swap out one of the days for an extra in Rome: 4 nights/3 full days is usually my recommended minimum for that one.
8/8: Rome, transfer to Florence
8/9: Florence
8/10: Florence (day trip?)
8/11: A.M. transfer to Venice (partial day)
8/12: Venice
8/13: Venice (or PM transfer to Rome?)
8/14 A.M. transfer to Rome (partial day)
8/15: Rome
8/16: Rome
8/17: fly home