Hi mmatloff-
Off top of my head?
Fly into Naples, 3 nights in Sorrento, home base for day trips (Should
I spend one night in Naples and one less night in Sorrento)?
3 nights is only 2 FULL days in Sorrento and you'll likely need them both to explore the region so no, I wouldn't spend a night in Naples.
ALL of your other 2-night stays will only give you 1 FULL day at each of those destinations, and Vernazza to Venice, for instance, is a haul that's going to eat up a good chunk of the transfer day
If you only have one FULL day for Florence, you'll eat that up day-tripping Siena and have little-to-no time for Florence itself. If you've previously been to Rome, I'd skip that one altogether and go directly to Florence from Sorrento: 3 nights Florence.
Accommodations in Vernazza could be a challenge to land at this point.. It is a VERY busy summer destination, and any still- available places to stay could be quite pricey. When looking for a room, make sure that it's IN town and not up in the hills or otherwise not within walking distance of the train station. Also look for availability in Monterosso, Riomaggiore or Manarola.
RS tours have the benefit of door-to-door transport that you won't have so every location change you make is going to take you longer. Personal preference but many of us find his suggested itineraries much too rushed but again, it comes down to personal preference.
If you plan to do any museum sightseeing in Florence, you'd need to make sure that the chosen museums are open during the short amount of time you've planned to stay there, and some involve advance, timed-entry reservations.