seating on the train from Rome to Cinque Terra and then to Florence

The trains on the short ride from La Spezia to Monterosso are very frequent so if you miss it get on the next one, meaning that is nothing to worry about.

That train station in Pisa has lockers so you can store the bags

I'm looking at it. The price you are selecting is actually 88 EUR from Rome to Monterosso. 80 EUR for 2 1st class seats from Rome to La Spezia and 8 EUR for 2 tickets (no 1st class) on the regional connection from La Spezia to Monterosso. But if you opt for the SuperEconomy tickets, the Rome-La Spezia leg is 69.80 EUR, saving you 10.20 EUR.

Yes, the seating is as you understand it.

For Oct 16, just buy tickets when you get to Italy, one set for Monterosso to Pisa Centrale and another for Pisa Centrale to Florence after you see Pisa. Validate the tickets for each leg before boarding the train.

A bit of advice- make sure you’re standing at the train exit with your luggage ready to get off when the train pulls into Monterosso. We were admiring the views so much that we didn’t even stand up until the train pulled into the station so by the time we got our suitcases and made our way to the door, it shuts in front of us and the conductor just looked at us, wagged his finger and shook his head. We had to get off at the next stop, Levanto, and caught the next train back. We waited almost an hour for the next train so that was an hour wasted of our brief 2 night stop in CT. That was a good lesson to learn.

Why should Trenitalia sell impossible connections?

If you miss a Regionale train, you can freely get on the following Regionale. Do not use a Regionale ticket on one of the few, expensive, Intercity trains from La Spezia to Monterosso. Conductors would fine you on the spot.

There are no lockers in Italian stations for obvious reasons, only staffed deposits.

Pisa S. Rossore station, which you'll pass on the way and which is close to the Field of Miracles, doesn't have luggage storage facilities. You'll need to continue on to Pisa Centrale. From there you can walk or take a bus or taxi to the Field of Miracles. The walk takes about 30 minutes, is very interesting and there are some good lunch places along the way (see RS guidebook), so I suggest budgeting time to walk either to or from the Field of Miracles.

Thank you all for the information.

We purchased regional train tickets at the same time we purchased tickets from Rome so we are ticketed all the way to Monterosso. We'll make sure we're ready to get off the train when it stops.

As for Pisa, we will take #651 at 9:07 to Pisa Centrale arriving at 10:17. We'll take the 30 minute walk after storing our luggage. We'll get lunch and take the 1:32 train to Firenze SMN arriving at 2:32. That gives us about 3 hours to walk, take in the sites, eat lunch and walk back to the train station.

The baggage drop at Pisa Centrale is near the end of Platform 1, to the right facing the station.

I checked

https://www.trenitalia.com/tcom-en

for your train, and the first class fare for two is €69,80. There is no such thing as a two for one offer. Are you using Italiarail or Raileurope?

I tend to over plan and that sometimes paints us into corners so, after thinking out loud and driving my wife crazy for the last hour or so, I think I'll wait to purchase the tickets from CT to Florence via Pisa.

We arrive about 4:00 in Monterosso and then have 3 full days scheduled in CT, leaving on the morning of the 4th day.

We can leave ourselves from flexibility by waiting to get the tickets from CT-Pisa-Florence in the event we take one of the CT days and take a half-day trip to Pisa.

When we do leave CT, that would get us to Florence earlier in the day on the 16th if we don't need to make the stop in Pisa on the way.

Looking at the train schedule, there appears to be several trains from CT to Florence so I don't think we will have difficulty getting there. That gives us several more hours in Florence on the day we arrive. We have that first day and then 2 more full days in Florence before leaving with a rental car for 4 nights at La Bruciata in Montepulciano. We can stop in Siena along the way or day trip back up to Siena.

I know we should have saved Rome for the end but it didn't work out - here's our itinerary:
10/06 Arrive Rome from Oakland, CA
10/06 - 10/12 Rome (5 full days in Rome)
10/12 - 10/16 CT (Monterosso)
CT is on my wife's bucket list so I wanted to give us plenty of time here to relax and enjoy the stay. Having said that, if we find ourselves with some free time to do something else, maybe a day trip to Pisa would be good. I know it's going there and back on the train so it does use up a few extra hours. there are morning trains that get us there mid-morning and would have us back early in the afternoon.

10/16 - 10/19 Florence (we will stop in Pisa if we don't take a half-day trip while in CT)
10/19 - 10/23 Montepulciano at a tuscany farmhouse.
We will have a rental car so we plan to explore the area. Day trip to Siena would be planned.

10/23 drive to Rome for departure on 10/24

Are there any recommendations to change that plan?

Thank you.

If you have done all you want to do in the Cinque Terre , take a ferry south to beautiful Portovenere for lunch and a visit. Then ferry back go Monterosso. All of the CT hiking trails were open when we were there, hiked to all 5 villages, used Monterosso’s beach, so three nights was more than enough time there for us.