Getting from Sicily to Amalfi coast by ferry, not flying, transportation logistics.

Take a direct overnight ferry from Palermo to Salerno: https://www.directferries.com/global/index.html. From Salerno take a train from Salerno to Puglia: https://www.trenitalia.com/en.html. Visit Sorrento on your way back from Puglia by taking a train to Naples central station. You’ll need to walk downstairs to hop on the Circumvesuviana train to get to Sorrento.

I found a couchette on the night train between Rome and Sicily an utterly miserable experience in 2015. The problem was that the couchette car jerked constantly from side to side, so I got not one minute of sleep. I believe we have at least one other poster here who found a regular sleeper car more comfortable.

You'd reduce your transportation time if you altered the order of your itinerary so you don't have to make a round trip between the Naples/Amalfi area and Puglia. Do you have time-specific commitments that prevent a change to an itinerary like this?

Palermo to Puglia (long trip; I'd probably fly) to Sorrento (fairly long trip) to Naples (very quick). There are two sort of gnarly transfers, but that's better than the three long travel legs you'll have if the routing is Palermo-Sorrento-Puglia-Naples.

Thank you for all information...I did not include details to keep it simple.
The ferry is probably the most practical from Palermo to get to Sorrento via Naples?
We are "resurrecting" a trip we had to cancel from last year, due to health issues.
We had AAA help us last year, and were not happy.
Tried another group this year, and also couldn't get what we wanted, so back to doing it ourselves.
First week in Sicily is already set (small tour) starting in Taormina, ending in Palermo (hence the ferry). The train sounds interesting, we tried to figure that out last year, but we'd have to get back to Taormina.
Second week in Sorrento/Amalfi coast, third week in Puglia.
We do have to return to Naples for flight back to US. We figured we'd need a day for travel in between each, and enjoy train travel, just not sure of best logistics in southern Italy.

You might wish to temper your urge for James Bond romance (which I like myself, alas) with the sad reality that powerful northern Italy has systematically starved "the south" of federal support and infrastructure dollars for generations. Long distance ferries are, to a large part, dinosaurs. To use your phrase, " the most practical from Palermo to get to Sorrento via Naples?", the answer is an airplane to Naples, then a car and driver to Sorrento. (Note: I have not done this. Slept in Sorrento five nights, for the good public transportation daytrips.)

It is also important to consider that a)Sorrento is not on the Amalfi Coast b)The Amalfi Coast is a bit hard to get to, and impossible to fly home (via FCO Rome) on the same-day c)Salerno is logistically farther from Sorrento than is Naples. (Opinion.)

What I'm asking is whether it has to be "Second week in Sorrento/Amalfi coast, third week in Puglia" as opposed to "second week in Puglia, third week in Sorrento/Amalfi coast".

All the info is appreciated, as well as perspectives;)
An additional question has come up, regarding bus v. train between Naples and Bari.
It seems that the bus trip is shorter, maybe more direct?
We've always taken trains, but there is only one direct/day, and it's still a longer ride than the bus.
Does anyone have experience with the buses, and what are they like?
Thank you.

I’d suggest you consider taking a direct flight from Palermo to Bari ( journey time 1 hour, 10 minutes) and thus switching your itinerary (as suggested by Acraven). and visiting Puglia after Sicily, and ending your trip in Amalfi Coast/ Naples.
You can check flights here: https://www.skyscanner.com/

In terms of transportation logistics, it would be helpful to know your complete itinerary.