I think that, as a non-resident of the lake shore, you're going to run into a problem with the riparian rights of those owners of lakeshore property, be they private or state, when you go to sinking a mooring. Riparian rights are commonly held to include the right to a view of the lake and your boat on it's mooring would obstruct that view. If you're anchoring, in transit, the navigation laws of the US as codified in the CFR would trump any riparian rights and allow you to anchor.
Your easiest option would be to find someone who likes the view of a nice sailboat moored off their shoreline and negotiate to sink a mooring there. With their permission, you'd be covered in being legal.
“Scientists are people who build the Brooklyn Bridge and then buy it.”
Wm. F. Buckley, Jr.