Again-it has been told here so many times: you CAN avoid some, not al, of the extraś-mostly by using the local/regional trains=means more sstops, slower, less comfort, maybe more changes.
For the superfast TGV N->P: there are several/day and IF you are lucky the extra cost is 10€ (small quota-often fully taken a few days ahead on busy days) or 20€-if not. Normal prices vary an awful lot in how far advance you book and for what tariff. There is also a HTL-saving overnight train again N→ P-couchette (lie down bunk) is 21,50 extra. Check for normal prices on their site-it will often suddenly turn into local lingo-to the detriment of those monolingual USAers.
Problem with TrenIt is that it is often very late-also with relaesing final data for times etc after summer timetable change on 12/6-and it seems all newbees want to plan too many monthes ahead.
But your overview of what tickets bought locally seems OK-can even cut it further down by also using Local trains Fi→ Ro. AND use also train instead of plane Ro->Ni. Up to you to decide what is best after all.
Explanation: In IT train fares are mostly quite cheap still and you only do 1 trip out of that, for which there are also ample lower priced alternatives. Global passes assume you visit a lot of countries-as the tipical 1st time USAer tends to do.
Oh”LOCal tickets, for the Regional, just buy when there from a machine=do not bother with these completely superfluous bookers that also charge extra. This also allows any last minute changes. IF you finally decide to do without pass-book direct on TrenItalia and sncf-the companies (well, state owned big burocratic institutions , also serving as large labour pools), this saves you a lot of hassle if anything turns sour
Please note that in Leonardo Express from Roma Termini to Rome Fiumicino Airport only 1st class Eurail Pass is valid, you can avoid this using regional trains to Fiumicino from other stations in Rome or with changing trains in Termini.