Ugh, hair is a pain and ESPECIALLY for NAHA! Their rules are really strict, absolutely no altering of the color of the hair - you can clean it up and clone strays out, but no dodging/burning, adding contrast or saturation, etc.
Mostly I zoom really far in and do a ton of cloning and a little bit of healing on a blank layer; I stopped using frequency separation entirely because it always seemed to go way too far way too easily, so I'm just super careful and do it entirely by hand now. Sometimes I clone in darken mode and sometimes in lighten, depending on the lightness levels or color, but mostly it's normal mode with opacity at 100%, flow around 40% and I keep the brush hardness relatively low - usually 20% or less, sometimes 0. I try to take care of most of the obvious flyaways but am careful to leave some because otherwise the hair starts to look fake really quickly. Sometimes all I do to "tame"close-to-the-head stray hairs is clone or heal them on their own layer, and then lower the opacity so that they're still visible but they don't stand out quite as much. This tends to be a bigger issue with people with lighter hair colors - at least for me, because I hardly ever shoot on a white background, but it could conceivably go the other way depending on BG color. For non-NAHA photos, I usually do some local dodge & burn via 2 curves layers, and then sometimes a little bit of global dodge & burn either on 2 more curves layers or sometimes a 50% gray layer.
Basically, it's a giant pain. lol
*edited to add: It's absolutely crucial, when taking hair-specific photos, to let your hairstylist interrupt your shooting flow to fix the hair as often as needed. And it happens a LOT. I have a great relationship with a couple of talented hair stylists, so we work well together on this, but when I first started doing it, I'll admit it was a bit jarring.