Ron.
First off, I’d say 7/3-8/3 would be the best time frame as june in new england isn;t necesarily the most fun time to be hiking due to the onslaught of blackflies as well as chilly nights and lingering snow at the higher elevations. Also much mud is on the trail. July is a great time to be in NE and specifically Maine! The best part of the AT. Why not start in Monson, the southern end of the 100 mile wildeness and hike south. At a very leaisurely pace you’ll hit Gorham in about 3 weeks and will still have a week or more to explore around the Whites. You can tackle the Carter-Moriah range being in very good shape and continue on thru the presidentials (if you wish to rehike them) or else maybe noodle around on some of the other non-AT trails.
You’ll get to start in Monson and set out your first night well rested if you decided to stay at Shaws and have Caratunk right up the trail if you need a break. All the Maine towns are great and this schedule would allow ample time to smell the roses and take a day or two off. You’ll havr some company coming south with SOBO’s and will run head into the front of the NOBO crowd.
Just a suggestion…
A-Train