Congratulations Cabinfever on your new island purchase. I am who has anchored a few times a season in a nice little cove around Timber (South Side, around corner from Witches). On a nice weekend it is often too crowded there for me to anchor so I understand your concern as an owner.
Now, what is the goal? How can everyone be happy? You are already educating us by posts on the forum. I sure will think twice about anchoring in that cove and won't go ashore now that I know it is private and it is your back yard beach.
How can you get people to keep their distance? The snake was a great idea. A swim rope was mentioned and I like that idea. You'll need a permit I believe. No one should anchor inside your swim line or swim in the area designated by the swim line. A raft would be nice too. With a few Private Property signs (on the raft too) may do the trick.
A less expensive approach would be to buy one of my specialty signs:
DANGER: HIGH VOLTAGE UNDERWATER CABLE - DO NOT ANCHOR and maybe put a big hose or conduit from the land to the water (to look like a High Voltage carrier). It's cheap
and may work. No permit required.
Let us know how we can be better neighbors on the lake and good luck to you.