I've run section A many times, and have always wanted to do Section B, just haven't gotten around to it yet. The flow is dam controlled, so it stays pretty consistent. In high snow pack years, they often will have a weekend in June where they let out a lot of water. You never know when that might be, but you could probably find out info from the fly fishing outfitters. You can't camp in section A, but there are quite a few designated river camps in section B that look really nice. Some are reservable through the rec.gov website. The rest you stop at Little Hole and sign up for. Check out www.fishgreenriver.com
for info, shuttles, pictures, camp info, etc. If you go all the way to Swinging Bridge/Crook Creek, I think that would be a nice long weekend float. bring your fly rod for sure.