That time of year is iffy, but I would make the trip anyway. Just bring a little extra food and make sure your bags are rated for the potential temps. I would go to Hazel or Deep because the trails stay on one side or have bridges at crossings, not too sure about Deep, but for Hazel this is accurate.
Flies have been covered. The campsites on Hazel are all good, but some distance. Proctor is close and nice as well. You won't see many people there that time of year. I do remember in 04 or 05 we planned on Hazel, got to the Fontana dock to take the shuttle and found that there had been some snow on the spine, the melt had caused the water temps to plummet, it was in the 30's and we bagged it that day. Hazel is pretty to hike around as well, sounds like you already know that. Get a book on the area, it may make the trip more interesting yet. Enjoy yourselves.