Potential Itinerary

I don't worry about train routes if I'm just trying to get from Point A to Point B. I go to the website of the appropriate rail company (trenitalia.com in this instance), identify my starting and ending points and let it tell me how to make it happen.

There's a good chance the October schedules will be rather different from what you see right now, but with luck the route options will be the same. The fast trains for October don't seem to have been loaded into the online schedule yet, so use a date in the near future for the day of the week you expect to be traveling to Venice. Your destination will be Venezia S. Lucia. Be careful about the time of day; the website defaults to the current time where you are.

I see a lot of trains that have just one change (in Florence/Firenze S. M. Novella) and take only about 4 hours, which isn't bad. It appears the reason the change-in-Florence route is faster than other options is that it gets you onto a very fast Freccia train early in the trip. The disadvantage is that late purchase of that rail ticket will cost you a lot more than you'd pay for a routing that keeps you on regional trains.

You can take a direct train from Firenze S.M.N. (Florence) to Lucca (1h 30m). Now to get from Lucca to Monterosso (Cinque Terre) you’ll need to connect in Pisa. You may want to store your bags in Pisa and check out the Leaning Tower and Field of Miracles before continuing on to the Cinque Terre.
To get to Venice from Monterosso you’ll need to connect in Pisa and Florence taking 6h 30m.

You might look at a change in itinerary.
This should cut down on travel time.

Rome>Cinque Terre>Lucca >Florence>Venice.

The itinerary change suggested above is a great idea.
Otherwise, I'm not sure about 3 nights in Cinque Terre, it might be 1 night too many depending on your interests, which seem to lean towards historic cities given the rest of the route you are planning. I would happily spend a 5th night in Rome instead, which could give you the chance to enjoy Rome at a more relaxed pace, or to do a quick day trip to, for instance, Ostia Antica.
No hard truth there, it all depends on your interests!

Thanks for all of the suggestions. I hadn't considered the Rome to Cinque Terre option, so I'll play around with the train schedules to see what that looks like. Usually I like to keep my train travel days to under 3 hours, but it looks like I'll have to bite the bullet if I want to include Cinque Terre (where I was planning on doing some hiking). The only other possibility I've thought about is skipping Lucca and going from the Cinque Terre (La Spezia) to Parma then Bologna followed by Venice which would cut down on the travel time. The pros would be that I would get to experience some less touristy places, but only spending 1 night in both cities might feel rushed.

The good news is reports are hopeful for your October trip, unless there's another surge. I was going to say something about devoting as much time to CT as you have, but I think if you spend the morning of Day 8 getting to CT and the evening of day 10 leaving CT you'd be about right. Otherwise, you've devoted as much time to CT as you have to Florence, and Florence offers way more than CT. I still vote for Lucca. Though not as small at hill towns like San Gimgnano or Volterra, it will give you a taste of a smaller community. Small town Tuscany is very different from Florence and has a delightful charm.

I hope your trip makes and have a wonderful time!

You could do this instead.

Rome 4 nites.

Cinque Terre 3 nites .

La Spezia to Lucca, (1hr 11min) either as a day trip, (luggage storage at the station) or 1 nite.

Lucca> Florence 4 nites, with a day trip to Bologna (38 min) , again you could spend a nite, but changing locations seems unnecessary.

Edit: forgot to add Venice

Florence > Venice 3 nites (2hrs17 min)

Traveling from La Spezia to Parma will consume at least 3 hr 45 min.
What we have found over 15 trips to Italy, is more or less straight line itineraries save time.

Hope this helps.

You may also need to factor in the weather in October.
In CT, there is not much to do indoors if it's pouring rain and you can't walk the trails in comfort.
The bigger towns and cities have plenty to do indoors all year round.
There is no predicting , of course, but I've been in Italy in September, a month earlier than you have planned; and been frozen in Venice one year, damp and wet weather.
Plan your Plan B for everywhere!

I would agree with Rome-CT-Lucca-Florence-Venice, to save backtracking.

Thanks all. I'm starting to think that maybe I'll save C.T. for another time based on the the feedback people are given me. Spending more time in Tuscany sounds appealing to me, where perhaps I could add time to Florence in order to take a day trip or two to Siena and some of the hill towns.

I agree you should save the Five villages for the next time.

If you change your mind, on June 13 the new schedules will be uploaded on trenitalia.com. Note that the "classic" train route from the Cinque Terre to Venice goes via Milano Centrale. Staying in Monterosso you'd save one train transfer.

Only those who drive prefer to cross the Alps via Parma.