Ok, quick question (not to be obnoxious, I'm just wondering): if improper mixing is the cause of many too-low gravity measurements, shouldn't one see just as many too-
high gravity measurements? As I understand it, if the wort and the top-off water are improperly mixed, then most likely it's more water nearer the top of the fermenter, and more wort neat the bottom, since wort has, well, a higher gravity than water.
But if you've just shaken the fermenter up for a few minutes and stick your turkey baster or wine thief or whatever deep enough in there, isn't there as much of a chance (or even more of a chance, if the ratio of wort to top-off water is greater than 1) that the hydro sample you end up with will have more wort than water in it, and will therefore give you a
higher OG than is really the case?
Also, really - 10 minutes? Jeez, that'll kill the back.
Maybe it's time to just bend up a coat hanger, sanitize, plug into a drill and go to town.