Just as a random point: the waterer doesnt have to be level. It's supposed to be level, but if you cant manage level, put the part that lets the water into the tray on the downhill side. it wont fill full depth all the way around, but it wont just drain out.
Depending on what the brooder walls are made out of, you could tie it down with just a loop around the middle/top of the waterer like the top metal band here
I put my chicks on an elevated mesh floor. The amount of poop they can peck at is significantly decreased and water would go through the floor as well. I've never had a waterer tip over from chicks though, I dont think. I usually use ceramic ramekins so they are relatively heavy and cant easily...