I go up there every year around the middle of July. My brother has a boat docked in Baileys harbor from July 1 to August 15. He has been fishing up there for 20 years and he always says the salmon fishing usually starts around the 4th of July and lasts until about the first week in August.Good Luck
In my experience, the area you're talking about (Gills Rock) typically heats up around late june to early July. Fish remain present through labor day and later. Are you planning on fishing port des mort, the bay side, or the lake side? The west side of Washington Island has deep water access. If you've not fished Gills rock before, you'll want to get familiar with the reef that sticks out to the west - it goes out pretty far and if you're not redy for it you'll lose cannonballs and other expensive gear.
If you need more info, feel free to PM me with ?'s