Possible to do Pompeii on travel day from Salerno to Rome?

You could just take a taxi from the Trenitalia station (where you arrive when coming from Salerno) to the site and store luggage there. Travel onward to Naples from there to change trains.
OR, time out what it costs in time to backtrack and store at Salerno?
Some people pay a private driver to stay with the car/luggage.

…and just to add another possibility, do you know about Paestum? It’s a short train ride from Salerno, and the Greek ruins are amazing! Plus the fresh buffalo mozzarella in that area for lunch.

@Jean - Yes we had considered shortening our stay in Florence by a day and spending an extra night in Salerno to also see Paestum. Currently have 3 nights book in Florence then 2 nights in Orvieto (e-bike tour one day) and then on to Salerno. Maybe 3 nights is too much in Florence and would be better to add a night to Salerno to see Paestum?

Thanks

If you do Pompeii on one of your full days, and do a hike and ferry ride on your other full day, it would be much easier to do a Paestum visit on your departure day.
In my experience, there was a shop offering luggage storage at Salerno train station (it could be in the vicinity now and not IN the train station). There is a short, flat, partially shaded walk from Paestum train station to the temples, but it is nothing like the several hours slog over big cobblestones that Pompeii requires (totally worth it and amazing!).

Read carefully this discussion of the opposite direction trip:

https://community.ricksteves.com/travel-forum/italy/train-from-naples-to-pompei-and-then-to-salerno#bottom

I’d advise (and regularly do advise) against Path of the Gods. I have more than few reasons, but mainly the time/effort commitment just doesn’t pay off imo. Especially coming from Salerno, you’ll spend a ton of effort and not see much of the coast. On your very limited time, it truly isn’t worth what you’d be skipping. Instead, take a ferry to Amalfi, grab the bus up from the dock to Ravello. Ravello is beautiful. From Villa Cimbrone you basically have the same views you do along PotG. If you felt inclined, you can hike down from Ravello to Atrani. And/or ferry further to Positano for a minute. The views from the ferry are amazing, and frankly beat PotG on that front too.

I’d hate to squeeze Pompeii in like this, but if you feel like this is your best option then I would do whatever you can to make it easy on yourselves. Taxi from one Pompeii station to the one with luggage storage sounds easy enough.

Another lovely hike that might better maximize your time is Path of the lemons, which you can take all the way to Ravello from Maori. We walked down from Ravello to Amalfi via Atrani, then caught a bus back, but I would recommend the ferry.
There are also some up and back loops out of Amalfi.
With both of those options, you can rely on ferry only or ferry + bus, whereas with POTG, I think you may have a harder time getting to trailheads.

Removing a day from Florence depends on what you wanted to do there and also what time you arrive there for the first day in Florence.

Italy was certainly busy with tourists in the major cities in May (less busy & relaxing in the smaller ones), so give yourself plenty of buffer time for anything that’s very popular like Florence, Rome & the main cities in the Amalfi area.

When I was there in Jan 23 there was baggage storage at Pompeii train station. It was right at the terminal. This is the station that the Salerno train and Rome trains leave from.

The walk was 20 min to the entrance. However you can also taxi and store your bags at the entrance.