You are right on target! This is logic..........no reason to involve anyone else. Simply wait a few days and start a search of that particular area. Even better if LE had brought in the cadaver dogs to search those woods.
I wonder why they never tried to drain it like they do lakes and ponds around here. They just did that to find the body of a guy who had been missing in Orlando for over a year. they did find the body once it was drained.