Pirate and the OP,
That's complete bull! We go to Tahquamenon Falls State Park every year in the late summer and fall and have for over 40 years now. All 3 CG's, Rivermouth, Lower Falls upper CG, and out favorite is the Lower Falls lower CG about 1/4 mile from the Lower Falls by trail along the river if it's not full. We never get reservations as there are hundreds of CG's in the UP to choose from and always find a site somewhere as we are flexible. Never had many mosquitos yet. Most times there were hardly any! Most mosquitos are in the late spring and after a rain when it's hot and humid.
To the OP! You may have a problem getting a site this close to Laborday as nearly all Michigan State Park CG's are full by reservations over holiday periods. Right after Laborday there will be sites available as kids are back in school but then when the leaves change, they can be full again as it's knock out beautiful in the UP and the LP too. Leaf change timing depends on the weather and night time temps. A lot of rain ruins the irridescent colors i the leaves but cold nights and dry weather brightens them up so vividly. The weather is something we can't control. The LP is usually about 2 weeks later than the UP in the northern half and 3 weeks later in the southern half than the UP. Snowfall doesn't happer until late October or later and if it does, it melts the next day.