TL;DR - You are probably OK to beach on private property on Lake St Clair if caught in a storm. If you use any private mooring facilities, you are risking liability for damages you cause. Also note as captain of your vessel, you have legal obligation to protect your passengers’ lives (including your own). “Life and limb” obligations almost always trump property rights.
Worth noting: There are varying definitions of what constitutes “the Great Lakes” and what is excluded. This is important as Great Lakes laws and rules are NOT the same as most inland lakes and waterways.
For example, in many cases the lakefront property owner of an inland lake has different property rights at the shore than does a lakefront property owner on one of the Great Lakes. There are many other small differences in the law that you might not expect. For one example, laws governing dropping off and launching skiers and other towables are very different (ask me how I know this!
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The USCG has primacy on the Great Lakes and they consider Lake St Clair to be one of the Great Lakes’ “connecting waters” along with the St Clair and Detroit Rivers, the St Marys River, etc. Shoreline case law on the Great Lakes is varied and somewhat conflicting but generally follows the “public trust doctrine” whereby public rights of fishing, hunting, and navigation are protected up to the “ordinary high water mark” (which is loosely defined as the place on the shore up to which the the presence and action of the water is so continuous as it leave a distinct mark). Rights to walk along the shoreline have a more mixed caselaw history.
In this sense, Great Lakes shoreline definition is analogous to the high tide line others have mentioned prevails on ocean shorelines. One big difference - Great Lakes water levels have swung by many feet multiple times over the last hundred years. The highest of Lake Michigan’s high water marks (~1930, early 1950s, mid 1970s, mid 1980s, 2019-20) was nearly 7 feet (!) above its lowest low water marks (mid 1920s, mid 1930s, mid 1960s, 2002-2014). Seven feet of water elevation can, in many cases, move the “ordinary high water mark” by many dozens of feet.
Considering all that: Assuming you can treat Lake St Clair shoreline like a Great Lake shoreline, you already have reasonable, legal “navigation access” to its shore. Beaching in a storm to protect human life would nearly certainly be legal. Mooring to someone’s dock and/or mooring ball in a storm is not so certain, and you would likely be liable for any damage your actions create (you have no way of knowing the test load of the chain under that mooring ball, etc.)
Strongly suggest reaching out to your local US Coast Guard Auxiliary for better references than a bunch of “Internet guys.”
