Last year from mid July into August for three weeks, I think the only place we recall that had a full sign was Grand Falls Windsor, per the other poster's same experience. It's a really nice RV facility mid-way on the long cross island drive. Plus there are seasonal locals in some sites there.
Also on some of the outport peninsulas to the north, like Baie Verte, there's not a whole lot of RV parks to choose from if/when you want electric hookups. But I don't think it would be hard to find somewhere to pull off for dry camping. Folks are quite friendly.
The advise about calling ahead would probably take care of your needs.
