Thanks, Chris. Yes, there are more transfer days than I would like, but 4 of them are with a private driver, so those days have at least one sightseeing stop (eg, Segesta and/or Erice between Palermo and Trapani, Selinunte and/or Scala di Turchi between Trapani and Agrigento, Villa Romana del Casale between Agrigento and Ragusa, Noto between Ragusa and Siracusa). That leaves 3 transfer days within the itinerary (not much I can do to eliminate the two other transfer days from and to the US except move to Campania or Sicily, which actually would be an interesting adventure but is not in the cards for me).
I looked at the ferry between Naples and Lipari, but in April it only runs one day per week, and that day of the week does not fit in this itinerary. I am considering adding the driver service to the Lipari-Milazzo-Palermo transfer day so we can make a pit stop in Cefalu before we arrive in Palermo, which would also eliminate one of the possible day trips from the Palermo list of activities.
Paestum is somewhat of an outlier that I added at the last minute-since we are taking the train from Naples to Milazzo (for the ferry to Lipari), we don't have the option of making Paestum an enroute sightseeing stop, so I added in a single overnight there. Mrs W and I both dislike single night stops (the least efficient duration), but in this case adding more nights resulted in an unacceptable reduction elsewhere, so I stuck with that plan. We will catch an 8 or 9 AM train from Naples to Paestum, store our bags at the hotel, and spend the rest of the day exploring the museum and archaeological site. Then we continue our journey to Sicily the next day via train (Paestum-Sapri-Milazzo), ferry to Lipari, then ferry back to Milazzo and take the train (or meet our driver) and continue on to Palermo
Trip plans that cover more than the sights of the base cities themselves always involve a trade between the "hub and spoke" approach (one base, day trips from that base), but in the case of Sicily (and Ireland, our trip this past April), the sequential style adds the benefit of experiencing smaller towns and villages that are much closer to the sights. After several of these types of trips (Ireland, Switzerland, Scotland, central Italy, Andalucia), we have concluded that the series approach (a mix of short and long overnights that are well positioned for our sightseeing) works better for us and is an acceptable compromise between the two itinerary types.