Popular area that is only growing in popularity, shortage of lodging options, all of Sept is still a very busy time there.
I suspect there are still good options available and I am sure Airbnb type short term rentals will have decent availability but some of the best value places being already booked does not surprise me. If you said the same about Oct I would be surprised.
You are talking about quite a few towns / large region so hard to recommend one place without more info,
I stayed at the Hotel Bel Air in Sorrento and the Hotel Eden Roc in Positano ; loved them both ; each with amazing views but not sure that helps.
I usually start booking stuff 9 months out for popular spots ; but also try to have as many of them as possible with free cancellation as I tweak my plans often around the 4-6 month mark ; as that is more common time to book flights.