transit strikes are the bane of travel in Europe. As has been said, you may not know until the day before if the strike will be called off.
@hiredman wrote: Check out Marino Bus. 07:05 La Spezia - 10:05 Florence
It would make for an early wakeup but the train R12213 leaves Monterosso at 6:20am and gets to La Spezia Centrale at 6:45am. On the map it looks like about a 1 mile walk to the bus stop for Marino bus. It would be tight, and the destination in Florence from the bus company website seems to be way out of town. So not sure this is a great solution. But the R12213 is on the list of guaranteed trains at https://www.trenitalia.com/it/regionale/liguria/treni-garantiti-liguria.html
The problem with piecing together a rail solution is you're crossing regions. So you'll need to find both a regional train that gets you to a larger train station, then a longer-haul train to Florence. And you'll need both of them to be guaranteed trains.
One option that works on paper is taking R12411 at 16:21 to La Spezia, arriving 16:48. This train is on the guaranteed list above. Then take R18407 to Firenze leaving at 19:16 and arriving at 21:57 This train is on the guaranteed list at https://www.trenitalia.com/it/regionale/toscana/treni-garantiti-toscana.html
But it sounds like a lousy trip; you'll arrive in Florence at 10pm at nite, losing the whole day. If possible try to go a day early or a day later.