I would tell you names of the quests, but my save is gone somehow... :(
But in short, I got enough wood to get the upgrade for water (80), then used it on water. But didn't have enough axes to keep producing wood. Since I didn't the 5 axes needed, I could not produce more wood. Since 3 wood is required per hardwood, and however many hardwood are needed for an axe, it's stuck.
Like you said if I had made it to the tasks, there is the chance that I could have been lucky enough to get a task which would reward me with wood. But if the task was to produce wood, hardwood, or axes, I would still have been stuck.
Why did you stop releasing a desktop version where we have access to backup our game save? -EDITED I say this because I played shortly after you released the game, checking back often for updates, until you took your break and then recently came and saw you had made progress.