I think it wasn’t intended but spamming the interact input on the wood chopping minigame allows to cut it in less than a second. I was gathering that wood fast!!! Felt good ahah. The game is super charming, well done!
Just tested myself; I think you're missing twice and hitting once, but you get wood for each swing that hits an unhit green field (Sonchou might be going without wood this winter haha).