From what you're saying... that they're not peeing in the veggies but only in the hay... I think they already view that cage as one giant litterbox. The only issue is that... YOU don't realize that the cage is one big litterbox.... lol! They know something that you don't know. Smart bunnies! Let us know how that works out for you, and more pics would be great! For 3 bunnies, you need a larger litter area so there is no competition over the toilet, and it'll be less work for you. With my two litterboxes, I clean them both out 2 or 3 times a week and that's it. It would be more work if I had one small litterbox that I had to clean daily. And with buns, the more opportunity you give them to be "right" (more room to potty) the fewer problems you'll have.
As far as the water bottle, I like having mine over the litterbox. One time I didn't screw the cap on all the way when I changed it and it drained out all over the floor. So if it's positioned over the box, at least if it leaks, the only thing that gets wet is the litter.