Hi there & welcome to the Forum! (PS, Many others commented in a similar vein as I was typing, does look like you've designed this for your priorities but I think we're agreed Day 6 from Venice via Pompeii to AC needs a re-think.)
Definitely look at a 'multi city' trip, where you fly into Venice for example & out of Naples via Rome, as this will save you a day traveling back to Rome & an overnight stay.
Day 2-3 - You only have one full day in Venice. Many on the Forum would suggest longer. And Venice isn't a quick train stop away, you need to get into & out of Venice proper, we took the ferry.
Day 6- Florence 🚂 Naples 🚙 private transfer to Positano w Pompeii stop - THIS is a very long day! Look at the train schedule, and driving from Naples to Positano, via Pompeii which in September will still be very warm in the afternoon, would be a drag. OK, about Positano, it looks amazing from the water, but it is extremely hilly, expensive & crowded. We stayed 3x in the town of Amalfi because it has a nice little walkable downtown and is easier to navigate. Or many people on the Forum skip getting into & out of this area just to spend the night & take a fast train from Rome (in your case from Venice) to Salerno. Spend 2 nights here & take a ferry UP the coast to Positano & back, relax & see all these lovely towns from the water, where they are viewed best.
I would suggest doing Pompeii at end of your trip to AC, you can hire a private driver from your hotel via Pompeii to Naples, where you'd want to spend the night if flight is early the next day back to USA. (If you stay in Salerno, I'm sure you can take a train closer to Pompeii & meet your driver there.) And frankly unless you hate museums, a visit to the Archeological Museum in Naples would really deepen your experience of Pompeii! And the food in Naples is wonderful!
Day 7- Positano (day trip possible, capri etc) - I would skip Capri for a day trip unless you're very keen. It will be jammed. suggest day trip by ferry up to Positano, back via Amalfi, lots of nice UPHILL hikes near Amalfi, and then there's the fantastic little town of Ravello, with the Villa Cimbrone & MEGA views out over the Med, accessible via bus. I've been to AC, Capri, Sorrento & this is by far my favorite spot in the area.
OR if you absolutely must stay on the AC, you could add a stop over in Ravello en route to Pompeii & Naples.
Hope some of that's helpful!