We may be heading out ourselves around then. As far as the GMC and “discouraging” use of the LT during mud season, it is discouraged in the higher elevations. Not the entire trail. We will be doing a 2 nighter later this week over in the Brandon Gap area.
As for temps, your target range is right on.
As for bugs and things, well… it is a part of the territory in NE. Best advice is to make sure you do two things - #1 Wear headcover(Black flies love to land in your hair and die) #2 - Wear DEET on exposed skin and refresh it every so often (especially around the ears,neck, hairline) to help stave off the Black Flies. The flies are bad nearest running water. They do not breed in standing water. So not everywhere on the trail will you run into Black Flies.
If we have to start around Memorial Day, we’ll update our journal on TrailJournals to indicate that. Maybe we can hook up with you. Otherwise, have a great hike, don’t be discouraged and do be prepared for the bugs 
Grinch