The R2R2R monikor is hard to type.
Anyone unclear on the route and mileage involved should look here: http://www.nps.gov/grca/planyourvisit/trail-distances.htm
A spring Double is a bit trickier than a fall one, because you'll be balancing not-too-hot temps in the inner canyon with not-too-much snow high up on the North Kaibab. The road out to the north rim is not reliably open and snow free until May, which IMO is too late for the Double temp wise. I attempted a Double Crossing in early February one year and turned around right before the big traverse through the Redwall on the North Kaibab because of deep snow and lots of ice. Anyone attempting this in February or March would do well to bring microspikes at the very least.
Late March and early April are probably the best times to do this.
For anyone desiring a shorter hike, the trip down the river and back is worthwhile. The shuttle along the south rim will be running, so it's easy to get from one TH to another. Going down to Phantom, out to Ribbon Falls, and then back up is a good long but not too long option as well.