My wife and I are in the same, figurative, boat. We will be in Florence May 16 and then were to leave May 19th to Manarola (via Pisa) in the CT. The national strike planned for May 19th throws that whole travel day into a huge problem because the trains to CT are regionale, and from what I saw are owned by the state (Trenitalia). As already posted, if you look at the "guaranteed trains" there are none/zero on Sundays because of the dates posted above: from 06:00 to 09:00 and from 18:00 to 21:00 Mon-Sat.
ItaliaRail
I've looked at the bus option like FlexiBus, but from what I could find on routes from Florence to La Spezia alone, there were only 1 or 2 buses running on May 19 and at terrible hours (like depart at 0200 or 1700'ish). I'm not getting on a bus at 2am to arrive in La Spezia at 6am. And if I choose the 1700 (5pm for us Americans) that gets into La Spezia around 1940 (7:40pm). Great, I'm partially to Manarola but if I wanted to use the ferry to the CT, last departure from La Spezia is 1520 (3:20pm) which is no where near late enough. So ferry from La Spezia really isn't an option.
CT ferry boat timetable
This leaves me with my final, ok maybe 2, option(s): rent a car or stay longer in Florence until strike is over. For me, I can only see the car rental as an option. The car rental will be pricey as I'm certainly not wasting my time returning it to the originating city, so they charge extra for being a one-way trip.
Then there's parking in Manarola, only 1 non-reservable parking spot outside the city and it's tiny, maybe 50 or so slots (sorry, I didn't count).
I guess there's one more option if I did make it to La Spezia at some off hour via bus service, take the Line 29 bus (from rome2rio website) or I guess a taxi.
Frustrated in Minnesota, but still looking forward to our 2 week trip to Italy.