How long does it take to transfer at la spezia?!

Your second plan might be the way I would go.

I'd never be sure if early morning commuters to work might hold the local train up a minute or two.

I've changed trains at La Spezia Centrale and found it easy but if you are worried you can get your early morning cornetto and caffé on that station while you wait instead of before you board the first train.

On the other hand, as you will be leaving via La Spezia can we assume that you will also arrive through the same station? Then you can see how you like it and decide on the day which starting train to go for.

Firenze SMN is a cake walk in 24 minutes.

On the other hand, as long as you were going to get the earlier train, you could connect at La Spezia Centrale to Freccia at 6:50 and arrive in Roma Termini at 10:03, depart for Napoli Centrale at 10:40 and eating pizza after 11:50. I'd think that simpler....

The regional trains in the CT often run late. I missed a connection because of that. Take the earlier train from Vernazza. There is a cafe at the La Spezia train station.

Why are you taking the only option that requires you the most train changes passing through the more expensive route via Florence? Do you like hassle?

There are plenty of options that require only two train changes (in La Spezia and at Roma Termini) which take the coastal route, one of them departs still Vernazza at the same time (7:12 am train to La Spezia) but then you would transfer to the 08:18 train directly to Rome, via the coastal route, without having to change in Pisa and Florence. With that option, you will have plenty of time to change both in La Spezia and Rome. There are also more similar options later in the day, staring at 9:24.
Then if you are willing to leave in the afternoon, there is one option departing at 13:14 with only one train change, in La Spezia, which takes you to Naples directly with no further changes.

Thanks for the input all! Roberto, I see the trains you are talking about. The only reason I chose this route is because once we get to Napoli Centrale, we still have a drive to Positano from there, and I want to maximize my time in Positano and not get there too late in the afternoon. This route, while it has transfers early on, at least gets us to Napoli Centrale before 1PM. Also, we'll have already been in Florence so I figure that station will be easier to navigate than Roma Termini?

There is a route via Rome that gets us in at 2PM, but requires transfers at both Roma S Pietro and then Roma Termini (so also 2 transfers same as my route). The more direct route which has just one transfer at Roma Termini gets us to Napoli Centrale at 2:30pm. I'm definitely going to think about your suggestion though to minimize transfers!

The option you chose via Florence departing at 7:12 gets you to Naples at 2pm not 1pm. 14:00 is 2pm. To translate the 24hr clock into the English time, you need to deduct 12 from the afternoon time.

The one I'm proposing departs at the same time and gets you to Naples at 14:29pm (2:29pm), so just half hour later..
Roma Termini and Firenze SMN are similar in design. They are both terminus type stations. The only difference is that SMN has 16 tracks, while Termini has 24. But the way you change trains is similar. You walk to the head of the track and look for the departing train. Incidentally changing at Rome may be easier. Trains coming into SMN from Pisa generally go to tracks 3 and 4, which stop farther back and therefore may require a longer walk to catch the frecciarossa to Naples (was working inside SMN during my "service")