You get 5 Axes from one of the quest rewards. Have you done the quest up until the one that unlocks the Tumor LORED? If so, you can do a task for whatever resource you're lacking to get un-stuck.
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.
You can abandon random tasks, so you can safely get un-stuck if you get stuck like that. I never anticipated someone would grind to upgrade Water before finishing the quests D:
2.0 isn't really finished, so I was just not updating both desktop and mobile, but there's no reason to not do that. As soon as I finish the next mini update which revamps the Radiative tree, I will resume updating the downloadable version.