Fluttering-about
In the Brooder
Consider a nipple watering system. The waterer hangs and it doesn't matter about the leveling. I use vertical nipples but they also come in horizontal. Research them. You might find that one of them solves your problem of water spills. Nipples may leak a tiny bit but not like spills you're experiencing.
How difficult is it to "train" the chickens to use a drip watering system? My chickens are so sweet, but no very smart..