What month to avoid the massive bug hatch??

Most years - bugs in the northern lattitudes can be bad from mid-May through June and some into July. Mid July and later are generally pretty good for weather and low bug levels.

Midges, last about a week or two. Only a problem near the water. By the 2nd week of June, they are gone.
Mosquitoes come and go, we're 30 miles south of the bridge, never used our screen tent.
Flys are mainly in the woods

February!

I go to the UP in Sept/Oct. Kids are back in school, less crowds and bugs gone.

LOL - I was born in the UP an bugged out. Mom's idea. Now I'm in bug free Fort Collins Colorado. Planning on getting back up there and will shoot for Sept/Oct (thanks @steveh27).

I grew up in MI and I don't recall any specific week of a hatch. There were just mosquitos every evening and early morning, unless the breeze was strong enough to keep 'em away. Biting black flies in the UP vary greatly in location and can occur any time during the summer, but if one runs into them one can usually find a fly-free place 10 or 20 miles away. Not familiar with the midges.

Of course, things have changed somewhat in the 3 decades since we moved away from MI (only returning for a week here or there during summer). For one, ticks were never a problem in mid-Michigan where I grew up and I could roam the woods freely without bug spray, but now I guess they're all over the state.

Two years ago in June I was up there vacationing. Skeeters were thicker than jam on toast at Fort Custer State Park, and a little bit pesky at Muskallonge Lake SP, but almost nonexistent at Seven Lakes, Petoskey SP, and Wilderness SP. So it really can be hit or miss IMO.