Dylan, I'm a bit late to the party, but being fortunate enough to live 2 hours from the big ditch, I get up there a lot. I've done R2R2R in a day many times (13-5 hours, typically). Here are some thoughts:
-There's lots of snow around this year. Much of the N Kaibab as is ascends is very shaded. I'd expect snow and ice in spots well into May this year. In late January of this year I got turned around ~4 miles from the rim by knee deep post holing at only 5000'! Also, bear in mind that the N Rim lodge is three miles away from the N Kaibab TH. This has come as a surprise to many dismayed backpackers. It is an awesome place, one of my favorite places on earth to kick back and have a beer.
-Water will be available at Phantom and the pump station residence (~8-9 miles north of Phantom) year round. I never bring a filter or pills on this hike. Spigots going up to the South Rim (on the Bright Angel ONLY) get turned on right around now, the one at Supai Tunnel on the N Kaibab around the beginning on June.
-The descending will get you. On a R2R2R hike pacing the first downhill is crucial, or you'll find that when you turn around at halfway your quads have mysterious stopped working properly. Even on an overnight hike, and especially for folks who can't or don't train on 3k+ descents, going easy at the first will make a huge difference.
-Related note: bring trekking poles. Period. They make a huge difference going up and down. I never go the ditch without, even on dayhikes with an 8 lb pack.
-Campsites at the bottom are typically a huge pain to get. Staying at Cottonwood is a good idea. Besides being a nice location logistically, its a beautiful spot with nice sites. Also relevant, before May at-large camping is permitted on the N Rim. Might simplify things, though I wouldn't want to haul overnight gear up there only to carry it back down!
-It's getting quite warm down on the bottom of the canyon these days. Pack accordingly (light sleeping bag, etc), and don't think that just because it's summer you won't get roasted in the heat!
Have fun. Don't hesitate to contact me personally if I can be of assistance. It should also be said that the ideal time for this trip, IMO, is late October or early November.