Do you know if there is much data out there on real-world gender differences vis-a-vis regression to the mean on IQ / SAT / etc. tests? i.e. is this based on statistics, or is it born out in empirical observations?

I haven't seen any, offhand. Maybe the testing company provides info about retests, but then you're going to have different issues: anyone who takes the second test may be doing so because they had a bad day (giving you regression to a mean from the other direction) and may've boned up on test prep since, and there's the additional issue of test-retest effect - now that they know what the test is like, they will be less anxious and will know what to do, and test-takers in general may score better. (Since I'm looking at that right now, my DNB meta-analysis offers a case in point: in many of the experiments, the controls have slightly higher post-test IQ scores. Just the test-retest effect.)