Two things: seems plausible even if it's not proven, because the scaling of stats that are 354 at level 60 are actually at a base of 858, so 22 of something at level 50 (341) ~= 55 at level 60 (858). Of course, one of the points where SE has made this difficult is that there's mysterious rounding magic behind everything anyway.
Other thing: Maybe not what you want to hear after doing thousands and thousands of swings, but the CI is still disappointing at n=3000. So for example, 94.5% / 3000 swings means there is a 5% chance it is outside the range 93.68% to 95.32%.
One more thing: no seriously, good work.