UPDATE AND APOLOGY FOR QUESTIONING YOU GUYS' METHODS
So I had some time today. Thought about some methodology you guys suggested. Got out the stir plate, used Jim's method, and did a MUCH more extensive series of tests. I also remembered that Jim thought that a lack of homogeneity might show up big time in the refractometer sample, so I took those readings FIRST right out of the beaker on the stir plate and THEN checked with the hydrometer. Well!
Result: very consistent for the most part, and even the apparent outliers, when included in an average of all tests, fall precisely in line with the result excluding them. I get a correction factor of 0.97, which, having gone through this, I accept. I will now trust the refractometer enough for on-the-fly assessment of wort in the mash and boil. But I'm still sticking with my precision hydrometers for OG and beyond.
Big Monk, Jim, guys, thanks for helping me get my head around this!