I trained from Florence to Levanto (the town above the Cinque Terre) last week. I needed to change only in Pisa but my train didn't stop in Vernazza. Anyway...it's still two separate tickets. The ticket machine spit out two separate tickets, one for each train. You can check the Trenitalia website price as one booking vs. separate tickets and I'll bet you'll find it's the same price or close to the same, not worth worrying about anyway.

So if you really want to get off in La Spezia, just book a separate ticket from Pisa to La Spezia and then one to Vernazza.

As for Pisa: while I agree it's not much of a destination and the Field of Miracles is incredibly tourisity and unpleasant, the Tower itself is not to be missed if you are an American tourist. I stopped in Pisa and don't regret it, just to see the tower, even though I didn't like the town.

(And was that a joke about seeing the Tower from the train? I wound up going through Pisa several times on the train and never saw it.)