I'm hardly a GC expert, but I have hiked down from the North Rim and back in June. From Cottonwood Camp up to the North Rim, you'll pass Roaring Spring -- which is where most of the park gets its water, so there will be plenty. There is a water fountain at Supai Tunnel, as well. Check with the rangers before you start for the latest water info -- and ask hikers coming down from the North Rim, as well.

We ended up hiking back during the heat of the day -- not recommended, but if you walk slowly enough, and take breaks on the shady side, it's doable.

My only concern about your hike is that you take some patches for those 1-gallon reservoirs. The Platy Patches work well, even when water is streaming out of a hole in the bag. Otherwise you are placing a lot of faith in a large water container.
--Ken B