You're a hero. I'd agree with all of your suggestions. I keep watching that gif and feeling physically unsettled with the first set, then there's a sense of relief with the second. Then physically unsettled again, then physical relief again. The difference a couple of pixels can make is really dramatic.
I feel you on being unsettled. The ones that were the worst for me placement wise of the ones I animated are Koji, Punky, Longlash, and Sharp. Narrowed and Suspicious don't bother me quite as much but the larger eyes are really noticeable because they come a bit close to the hairline. It's actually a little more unsettling with a hair that's got side bangs or a slightly lower hairline. A lot of the unlockable hairs make the eyes look extra high.
A couple of pixels is noticeable when the face is only around 43 pixels tall (measured from the bottom of the widow's peak on buzzcut to the chin). Some hairs give a larger face (46 pixels for the hair I'm wearing) or smaller (40 on delish pio).
I just hope at least some of them get shifted because I actually really enjoy the art of the revamps.
Also agreeing with pandemonium's edits. Such slight shifts, but they make a huge difference.