Hi Steve,
My hike was in early October, 1998. Started at just before sunrise, and reached end of North Kaibab ~ 1 hour after sunset. Time table for Oct., 1998 says only 11.5 hours of sun, so my guess is max time was 14 hours. More likely 13. I did not eat enough (one orange, and one sandwich all day), my nephew was with me (~14 years old) and I ended up having to share my water with him, so finish was painful. Really impresses upon you the importance of fuel and hydration.
My brother, who lives in Phoenix and has done this hike a few times, cautions that the inner gorge can be triple digits in May, so recommends you go early.
Enjoy!
John