Just about everything up to the treeline is fair game as that's where the ACTUAL high water mark is. I've got a picture somewhere of ships aground with the masts in the trees, and buried up to the deck with sand.(think it was the Deer Park area) So don't let anyone BS you. Some realtors think the property line is closer to the water and ends at the grass. You will find logs washed up into the grass to the treeline, so that's the real high water mark. You'll notice a color change in the sand. It changes to white at the high water mark. Inland of the high water mark you can have mineral claims and property rights, but past it, no rights.
You may need a pump permit, unless you have riparian rights to Great Lakes waters. I am a riparian owner of Great Lakes waters, so I can pump as much as I want, but it must return back to the Lakes, under the Great Lakes Compact. But if you're from outside the compact area, you will need the permit to pump out of the lake. The Compact is an international treaty so it trumps local game wardens.
Keep your gold in your cons till you get home. They won't be able to determine how much you've collected. If you're on real good ground, you might hit the 15g limit.
Get pyrethrin fly spray for horses, spray yourself down with it. It will keep the flies at bay. That stuff will slow up a horsefly enough that you can smack the living S#%& out of that sucker! Get yourself wetsuit boots and high waist pants. The flies give up on the neoprene, it keeps the sun off, and it's great for wading in the lake.
If you can find the Sportsmen's Connection map book for Northern Michigan, BUY IT! It will show public lands with pretty good accuracy.