Hi and a warm welcome to the forum!
First off, the itinerary I'd choose would be the one with the most attractions/activities of interest to the two of you. Very gently, I'd put the idea of 'seeing Italy more as a local than a tourist' out of your head as practically ALL the destinations you've listed are 'touristy' locations....meaning many thousands of tourists visit them every year. That said, they're certainly not lacking in authenticity, such as a Disney park or other attraction built recently (in the big picture ) and/or specifically for tourism. Tourists flock to them because they are interesting, beautiful, have rare, very old treasures to marvel over, or all three.
Even Italians play tourist in their own country; visiting cities, museums, country and seasides that offer something different from their places of residence. So, there's not a thing wrong with being a tourist 'cause that's what we all are when we're traveling away from home for pleasure. :O)
Just a couple of comments off top of my head:
The CT will be slammed with visitors and I'd personally drop this one unless you are going there to hike some of the less traveled trails.
If keeping itinerary #2, I'd do Lucca as a day trip from Florence. Also, I dearly loved Florence but it is very heavy on Renaissance art, architecture and museums; things I enjoy very much but you might not so something to consider? It does make a very good base for a number of day trips but, well, to keep it or not depends on your interests.
Positano is expensive and frankly not very interesting other than for some snapshots - - we were done in 1/2 a day - so if you kept #3, I'd choose a different base. Sorrento, while next to but not ON the Amalfi Coast, is a good one for day trips to that one, Pompeii and Capri. Naples is fine for day-tripping Pompeii and Herculaneum and holds onto a gritty authenticity which visitors seem to love or hate. It has a highly regarded archeological museum and some other fine attractions but it's inconvenient for Positano and some other locations.
Rome has so much to offer that you'll just scratch the surface in 3.5 days, unless most of those things are not your cuppa tea.
All said and done, I'd probably go with the "Holy Trinity":
Venice - 3 nights/2.5 days
Florence - 4 nights/3.5 days. 1 day trip IF you need time to enjoy what Florence has to offer; 2 day trips if not.
Rome - 4 nights/3.5 days
Venice is not Florence, is not Rome. All three are very different cities with unique backgrounds so it's not as if you've seen one, you've seen Italy. Anything less, time-wise, will cut into unplanned wandering adventures you plan to do. Understand that the most visited of the museums, archeological sites, etc. will involve advance, timed-entry tickets so that's going to affect a certain amount of spontaneous sightseeing.