Shipwrecks in Black Forest and Swamp yield a lot of fine wood, but they are at least uncommon if not rare. They can be found in shallow water, so coasts, rivers, and watery swamp areas. Destroy them with a weapon.

The towers with a wooden roof and a lot of dwarfs outside, in Black Forest, always have a wooden stool you can destroy to get 1 fine wood. Likewise, some of the towers have a table and a bench inside, which you can also destroy to get fine wood. Some Swamp cabins also have furniture.

Trees are the most reliable method, by far, though. My current world seems to have a lot of shipwrecks but that is just good RNG and nothing to rely on.

If you can handle the gobbies, plains are nothing but birch.

And of course since you have seeds you already know that the meadows has a decent splattering of birch/oak.

I wish they would have some of the 1 and 2 star greydwarves drop fine wood.

Not really. Just pick up the Elder's buff, get into the Meadow forest and keep them rolling. Compared to simpler wood, you don't really need all that much Fine Wood.

Just farm and plant oaks
Its the best you can do at that stage

Yeah I did the oak farm a lil bit. It's not like you need a lot of fine wood as long as you dont wreck longboats often. Once you arrive at the plains .. it really is no issue anymore.