In hindsight, you're probably right about the timer. I think I implemented it because I wanted there to be at least an idea of pressure as I couldn't imagine anyone taking more than 5 minutes, but perhaps no idea of pressure would have been better.
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).