Conure-
If you wanted to stay cooler, as mentioned, a bit later start would be better if you are going NOBO first. I agree that May/June is a bit early to hit the Northwoods. Not impossible by any means, but certainly not ideal. You will see very few folks. May, June, July would put you in better shape heading through VT, NH, Maine. You'd likely run into the southbounders starting, but no biggie. You'd get to VT near the end of the worst mud and likely only flirt with black fly season. But then you've got a hot stretch heading south from Harpers Aug, Sept, and if you're lucky fall colors to finish in Oct. but you'd likely miss them to be honest. You'd also likely miss the summer wildflower bloom in many areas.
I'm a bigger fan of going SOBO from Harpers and leaving earlier. April (or even march if you wanted), May, June to Springer, then Harpers on North for July Aug Sept. (Or June, July, Aug if you start in March and wanted to avoid PA in July) Northwoods in the late summer and fall has to be one of the prettiest around. You have to spend July somewhere, I'd pick PA over VA anyday. The best flowers on the trail are generally springtime down south, the best colors are hands down up north. Speaking seasonal beauty you can't go wrong. You will pass the bubble heading south, but not fight them for space much as most drop in the first month or so before you'll see them. You may find yourself with some NOBO's on the back end, but the herd will be seriously thinned, and three months in you may appreciate the relatively limited company. Finish at big K is a nice bonus, as is scooting over to the Long trail if your feet are still itching or you finish a bit too early for the fall colors.
All of the above assumes a six month pace- however, starting in the middle of the trail, in the easier terrain, makes building your trail legs easier and faster; so if you want them- bigger days will come faster than a traditional NOBO or SOBO hike.
In addition, southern services can thin out or even close up as the season is long over. If you aren't doing maildrops you could find yourself struggling a bit to find stove fuel and other common items as the folks down there tend not to reorder supplies late in the season. Some hostels and other services are limited as well. Going south first assures you that you'll be travelling in both areas when all services are available.
I would seriously consider HFGA HFMA, not sure what the ATC calls it but I call it Having Fun to Georgia, Having Fun to Maine- and it's the best hike in my not so humble opinion.
best of luck