I'll preface this post by noting that I have searched the forum and haven't found this route, which may in and of itself be a warning that it's not possible.
Travelling from Praiano to Rome mid-May, the following plan seems to work. I would appreciate feedback and comments.
Bus/taxi from Praiano to Positano
Ferry from Positano to Salerno - seem to be 3 options, NLG, alicost or Lucibello
Train from Salerno to Rome - Italiarail
You could also taxi or sitabus to Sorrento
At Sorrento catch the Campania express to Naples
At Naples catch trenitalia or italotren to Rome.
Instead of going further South to get a connection to go North
This seems reasonable, assuming you're not going to FCO in a hurry, and you don't mean to see Pompeii on the way. Note that mid-May is already busy, so you can expect crowded busses. I haven't taken those ferries but it wouldn't hurt to buy them in advance. Note that Frecciarossa trains get more expensive as departure approaches, but discount tickets can't be changed or refunded. They are really fast trains, for Italy.
Note that Italiarail is not a train company but a third party reseller that marks up the price of tickets. For trains from Salerno or Naples to Rome, use either the Trenitalia or Italo websites to buy your tickets, or buy them at the train station. The Circumvesuviana is a local train, and tickets are purchased at the train station.
You could also take a bus/taxi to Amalfi and ferry from there to Salerno, as ferries going from Positano to Salerno will generally stop at Amalfi. Bus/taxi could drop you off right by the ferry dock in Amalfi, whereas that may not be the case in Positano (especially for the bus - fairly long walk with many steps).
If you need a driver, I used Gennaro Risposi in Praiano they are located there. Great people, let me know I’ll be happy to share their info. Enjoy it’s a beautiful place!
