I believe there's a bus from La Spezia to Florence but getting to La Spezia itself could be a challenge. I'm sure the taxis will be circling and probably charging way too much but if you can get a larger city a bus may be an option.
Check out Marino Bus. 07:05 La Spezia - 10:05 Florence
Leaves: V.le Italia c/o Chiosco Palme by the cruise ship dock (I doubt the ferry is running early enough for this) and by the Tram for getting into Florence proper. Honestly not great options but it seems to be an option.
I'd check other places like Flixbus too.
To cover the whole distance the only other thing I can think of is an NCC driver or a tour company that offers transportation.
Hopefully the strike won't happen - they are never certain, good luck,
=Tod