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