I'm not sure In your urw folder, there's a file called diy_glossary.txt, it shows which crafting items increase timbercraft. It looks like wooden stake and staff, but they have a penalty that makes it harder to learn from. still, you could chop down slender tree trunks and make wooden stakes or staff and expect to get some skill increases. you can get up to 3 per day, but the first easier than the third.
Otherwise, you can get skill increases from chopping down trees. make them into logs with the stone axe before you make them into blocks, because that's three chances per tree -> trunk, log, block. if you go striaght from trunk -> block then you miss one of the chances for a skill up, and your trees are limited on the island so that matters. make sure you leave at least four trunks for the raft and paddle, don't use all your wood. you can do this on neighoburing islands, as well. There are a few you can swim to.
If you're open to playing with mods, you could install one of the older versions of BAC, I remember a bug that trying to make modded boards, which was still impossible with the stone axe, would give you skill ups even though you never succeeded at making boards, but i forget what version it was fixed in. But of course if you're open to mods then you can solve the whole puzzle that way, too, add a "rough board" item that takes 8 hours to make and only yields one board from a whole trunk but is still possible with a stone axe. If it were me, that'd spoil the excitement of trying to do almost impossible thing and maybe succeeding or maybe drowing with the shore in sight, but if you are bored and are starting to hate the game then it's a good option, you should always try to have fun and not be bored when playing.