Rangersedge,
I am an Illinois resident but owned a "private lake" in Wisconsin. In my experience very few people can explain the different rights to ownership of fish and of course the water they swim in. In my case I stocked my lake, paid taxes on the ground underneath the lake and maintained the water quality with aeration. it was a 40 acre "pond" and it was teeming with fish. The neighbors were frequently on the lake and fished it heavily.
After consulting with 3 attorneys on trying to somehow enforce no fishing I got nowhere.
Perhaps the crux of the Illinois situation is within the words:
"there may be some kind of property or personality dispute between you and nearby residents."

Maybe the property boundaries and or public right of ways are not clearly established...maybe there is a navigable stream running to the "private lake" and any stream like that would provide access.

I was told once that theoretically anyone can sort of parachute onto any body of water and legally fish it regardless as to the ownership of the land surrounding the water as the water is indeed not owned by the property owner. The fish might be sort of difficult for as we know some are in their from our stocking but others seem to come in from all over the place