1 Month Sicily Itinerary Help

Hi folks, I'm currently planning a 31-day trip to Sicily starting in early August and would like some help deciding upon the bases I should use, and the length of time that should be allocated to each. I'll be flying in and out from Palermo and plan to utilise public transport instead of driving, which has been a major factor in putting together the provisional plan I have here.

The list of regions/towns/attractions I am interested in visiting include:

Palermo/Monreale
Trapani/Erice/Egadi Islands
Agrigento/Valle Del Templi
Villa Romana del Casale
Val di Noto Baroque towns - Noto/Ragusa/Modica/Scicli
Syracuse/Ortigia
Catania/Mt. Etna
Taormina
Aeolian Islands
Cefalu

I currently have the following itinerary in place:

Palermo - 5 days
Trapani - 4 days
Agrigento - 3 days
Ortigia- 5 days
Catania - 4 days
Taormina - 3 days
Aeolian Islands - 4 days
Cefalu - 3 days

In order to keep the trip at a slower pace, I would ideally like to make use of a fewer number of bases and make day-trips to towns/points of interest in the surrounding region over doing shorter stays. So far, I am planning upon utilising Palermo and Trapani as bases from which to explore their surrounding regions. I would like to visit Valle dei Templi and am considering making Agrigento a base for a few nights, but am questioning the need for introducing the extra base as, outside of the Scala dei Turchi and maybe a day-trip to Sciacca, I'm not sure there's much in the surrounding area that I would be interested in visiting that is easily accessible via public transport. I understand that Agrigento can be reached in two-hours via public transport from Palermo, so is it still worth staying making Agrigento a base, or could I just make the day-trip to the Valle dei Templi from Palermo?

From my research, the only major city/base that I have under consideration that offers a direct route to Piazza Armerina to visit the Villa Romana del Casale is Catania, with the bus journey taking 1.5 hours each way. Is there a more convenient/alternate base from which to visit the Villa, and could it be visited from Agrigento?

I am planning on staying in Ortigia for one of the legs of the trip, and am wondering if this would make for a suitable base from which to visit the towns of the Val di Noto. Would I be better off introducing a dedicated base in the region itself such as Noto or Ragusa from which to visit the rest of the towns? I see that all of the towns I mentioned above are on the same train line, though the furthest (Ragusa) is over 2 hours on the train from Ortigia. How many days would I need to see the 4 listed (Ragusa, Modica, Noto, Scicli)? If only one or two, then maybe Ortigia would suffice?

On the final leg of my journey, I either plan to travel from the Aeolians to Cefalu to spend the final few days of my trip before flying home from Palermo, or I could rework the itinerary to travel straight to Palermo from the Aeolians and allocate the days I had dedicated to Cefalu elsewhere. Is it worth spending a few days in Cefalu given the provisional allocation of days that I have laid out here or could they be better spent on a longer stay elsewhere? Could and should Cefalu be done as a day-trip from Palermo?

Is this itinerary too ambitious? Would I be better off cutting down the number of bases and travel days involved? How would you reallocate the dispersion of days?

Many thanks!