I have this exact same tiny beach. I despise it. I planted a single coconut tree there and called it a day.
One time, my daily bottle spawned there and I drove myself crazy checking and rechecking all beaches until the tiny beach came into my sight by accident and there it was. So now I have to check it when I'm doing my eastern beach run...
It doesn't bother me enough to reset though. I'm a lot less particular than some people here about the details of my island