LOL, I think I just answered this question for you on PBF ... but I'll post it here too in case others are interested.
I haven't visited in late June ... but I have been there the first week or two of July for the last few years.
I understand that the black flies peak in June, but they are basically gone by early July. In early July the mosquitoes are in full swing. Fortunately, they respond to DEET, and I've also had success with the Picaridin in Cutter's. That said, I usually minimize the chemicals by relying on long sleeves and a bug net when they are swarming.
I would definitely bring a head net in June. Black flies don't seem to care about DEET, and if they are swarming when you are there it will be miserable without protection.