Haven't done any touring on the Big Island, but have ridden quite a bit around Captain Cook and Kealakekua Bay. Not much shoulder on the highway from N of Captain Cook to about 15 miles S of there. After that good shoulder pretty much all the way to Hilo. Traffic isn't too heavy, but over 50% tourists who are generally looking at other things besides the road. Lots of up and down all the way around. Lots of humidity which will sap you, so don't plan long days for the first couple. You mentioned a sleeping bag; I have never done it but I understand camping is pretty problematic; not many official spots and those are expensive. Don't know about stealth camping options.
Here is the only real Hawaii bike resource I have found online: http://www.pathhawaii.org/links.htm