There are lots of cheap rooms and at least a few campgrounds near all the rivers that have ZEC water. Those are almost the exact dates that we fished the Gaspe last year. We went all the way east and fished the York and Dartmouth. If you stay in Gaspe (the town) both the Motel Adams and Motel Fort Ramsey have rooms that are quite comfortable and reasonable. In addition, Fort Ramsey has a small campground right there. It is better suited for trailers or motorhomes, but there are a few sites that would work with a tent. The runs were quite late last year so none of the three of us ever saw a fish during those dates. However, both the York and Dartmouth, as well as the Ste Jean (though less so) are considered to be early rivers. Your other option that I'm familliar with would be to head to the Matapedia and stay with Peter Dube at the Motel Restigouche.
Maybe others can help you with some of the other rivers. All I know is that fishing is often better later in the month or in July on many of the other Gaspe rivers.