Glad to hear you own the entire lake property!

I have expertise in erosion, not in stopping it within a pond. Hopefully, you can get an expert to address that issue.

How expensive was your shoreline rock? I think a big berm of that would be pretty effective.

Maybe install some fabric by hand in the water, just beyond the current edge of your sand. Have a few dump loads of your shoreline gravel dumped right on the fabric. (If they can drive there without getting stuck. If not, then place it with a front-end loader.)