Given two things; we have the same weather as you, and the way that your boat is rigged, a big genny could not be trimmed in far enough to provide any value upwind, and it's too heavy to stay afloat downwind. The Hunters are not designed for it. That said, a large (very large if you want) asym is an excellent choice for the kind of Oilberta breezy days we're talking about. The look of the lake in your picture is same as the look of the lake in mine.
Our kite is probably close on 40% larger than it should be. If it were used in a real air, it could be a problem, but the cutoff is 12kts, and not at all if it's shifty and gusty.