Alright, I figured out my rookie mistake. Incidentally this is the first thing I'm ever typing with my new $450 keyboard.
There's a reason the guide asks you to watch a video and listen for a specific sound: it's a way to determine the
exact,
precise sound one of these Model F's is going to make when the keys actually work. That being said, it's a terrible way to figure it out. Chances are at least one of your keys actually registers if you've tried seating them all, so instead of watching that video, I instead suggest pressing that single, working key a few times and listening extremely closely. You hear that yoinky-sploinky? That characteristic chuh-pang when you press in and release the key? That's the sound every single key will make when it works properly without exception.
I'm serious, the sound is
that precise and telltale. You will hear a lot of thunks, a lot of things that are
sort of like the right sound. You'll swear you got it a few times. These are siren's lies, do it over and over until you get that right tactile sensation (and noise) with a key press. You'll know it when you get it.
But why does the guide suggest holding the board vertically? By default most of my springs were seated well (with a few exceptions), but when you have the board do anything
except lie horizontally it makes those springs stand directly out of the keyhole like little rows of uniform soldiers. Obviously twisting your keyboard in one direction may not put the springs at this super-precise angle, so spin it around until you think it's as close to centered as possible.
If your spring isn't standing out, straight and directly out of the middle of the hole, use this method to gently pull it out and press it back in:
https://imgur.com/a/6bnzW
Yes this will also take a few tries. You spent upwards three-hundred bucks on this thing, she has high standards.
But why do you want that to happen? Because if you look inside a key with your phone's flashlight, you will see an extremely precise little nub that the top of the spring 'locks' with. That's the secret of how this space-age technology from 1985 actually works. When you grasp that, the process of seating these keys is easier. Hopefully this post saves someone an hour of frustration getting their latest splurge to work properly.