Re: how do you measure a change of 1/10,000 of a proton diameter with a laser?
What you propose to measure is a water wave, not a gravity wave. Gravity wave is a "a change" in gravity force, or even better, a change (dynamic, propagating) in the the "shape" of the time-space. Like shrinking and stretching of the peek traffic on a highway. Yes, your moon does cause gravity waves hitting earth, but with a frequency of 2 per day. Does not make for good study. Kind of like measuring the speed of light with your torch and a handheld stopwatch.
A kid in Montana could explain things, if the identical signal was not detected at the other end of the continent.
Results are too precise? They pre-calculated several thousands of possible wave patterns the black holes could cause, in variety of scenarios. Among those patterns they found the one best matching what the detector, well, detected. Then they tweaked the inputs (masses, distances and rotation frequencies, and other stuff I don't understand) into their pattern producing model till they got the near perfect match. And voila. And it's not really that precise. Some things (like spin of one of the black holes) they can't say match about, many different values can match the produced pattern.
Of course the model they are using might be flawed. Of course you can dispute this, but you better know your stuff (and there's crapload of it) if you want to do that.