I think I might have a possible explanation for some of what's happening. Keep in mind I do not own and also barely ever play the game, but from what I know and have read here I have a theory that seems to follow along with the testing in here:
If it's truly not possible to 'fastfall' while moving upwards or at least increase your downward acceleration by tapping down then I'm thinking the results of many of these might actually be caused by 'SDI'ing outside of hitlag (it'd be more like smash air control or something but I'll just write it as 'SDI' as opposed to just SDI without the apostrophes). Particularly the vertical KOs. For horizontal I can see it also being aided by the faster aerials allowing you to jump/air control sooner, so with those it'd be a combination of the two.
Having not experienced it from playing the game myself and being a Melee player, such an idea of 'SDI' when not in hitlag would otherwise sound kind of silly to me, but it seems like it may exist in some form in this game. Whether or not it exists in the first place and it's really at work here I can't really say, but it certainly looks that way to me if you can't fastfall or something to similar effect when moving upward.
You know how MK's infinite dimensional cape works? The general way to do it is to hold downward and tap up on the c-stick (must be set to smashes I think). When in the startup of the move you can actually reposition yourself by smashing in that direction (like SDI). A little quirk is that when you move into the ground when doing this during the move it extends the cape's animation. By holding down and tapping the c-stick upward you 'SDI' into the ground when the c-stick is released, which extends it each time you do. You can also reach up onto platforms with it if you 'SDI' upwards before ending it.
So it would seem like the game reads it like this:
The way the game inputs the C-stick is like a tap on the control stick plus A, so this is what the game read:
Frame x-2: tilt down
Frame x-1: tilt down
Frame x: tap up + A
Frame x+1: tap down
Frame x+2: tilt down
You might ask, "If that actually happens then wouldn't that just make you 'SDI' up and then 'SDI' back down again which would cancel it out?" It might, in which case the 'SDI' isn't what's causing it. However, I think it may be combining the respective axis values that are input for the purposes of SDI, so when the c-stick is pressed up while down is being held on the control, it's really doing:
{[Y-Axis: -100] + [Y-Axis (from c-stick): +100]} / 2 = Y-Axis: 0
So as far as SDI input goes you'd be doing: Holding Full Down -> Neutral -> Full Down (results in a SDI down)
Also, check out this thread about non-hitlag 'SDI' which got me thinking:
http://allisbrawl.com/forum/topic.aspx?pid=299323#p299323
All you have to do to test my fast falling claims is simple. With DK and Mario in group brawl set Mario's damage to 230 via handicap and go to final destination. Up throw mario with DK and Mario should die. Holding down with Mario on the next up throw (after dying with DK after each up throw) Mario will die. Doing another Up thorw on Mario HOLDING DOWN and pressing a for a dair and he will still die. Next cstick (set to smash) a dair with Mario and he lives. Next cstick any other aerial and he will die. Next hold down and cstick any aerial except a dair and he will live. Next hold down and cstick a dair and he will die. Every time Mario lives you will notcie something. Mario is fast falling...
This is what caught my attention in this thread. Particularly the parts where holding and not holding down got different results for the same c-sticked aerial. Did anyone confirm each of these specific examples? They all follow the c-stick 'SDI' thing pretty well. The common factor with all of these is that a smash down is input when they live and is not when they die.
1) Up throw mario with DK and Mario should die.
No 'SDI'
2) Holding down with Mario on the next up throw (after dying with DK after each up throw) Mario will die.
No 'SDI'
3) Doing another Up thorw on Mario HOLDING DOWN and pressing a for a dair and he will still die.
Down is never smashed here. It is being held down the entire time.
No 'SDI'
4) Next cstick (set to smash) a dair with Mario and he lives.
The c-stick smashes Down + A.
'SDI' Down
5) Next cstick any other aerial and he will die.
The c-stick smashes a direction that is not away from the blastzone + A.
Useless 'SDI'
6) Next hold down and cstick any aerial except a dair and he will live.
Releasing the c-stick has at least a change of -50 for SDI on the Y-Axis and you 'SDI' down. You should also 'SDI' left/right when you press the c-stick if you F/B-Air.
'SDI' Down
7) Next hold down and cstick a dair and he will die.
Same as 3. Down is never smashed here. It is being held down the entire time.
No 'SDI'
OK. Now with the test with Zelda's U-Smash and Zamus in the video you were holding down on both right? When you did the D-Air this wouldn't have resulted in a 'SDI' and so you died just like number 7 above. When you did the other aerial (I don't know what move that is) you would have 'SDI'ed down when you released the c-stick which made you live like number 6 above.
On that note, did you release the c-stick when you did the aerial that saved you in this situation? If you did, could you also test the same exact thing but instead continue to
hold the c-stick in that direction the entire time after pressing it for the aerial? If doing that makes a difference then it'd mean that either non-hitlag 'SDI' is probably taking place and helping you survive or it's causing some kind of 'fastfall'. If it's the same and you live with both, then either it's not what's causing it or that the way I'm thinking the game reads the 2 sticks' inputs isn't right and it's still giving a tap down input somewhere.
With the examples above it seems like the deciding factor that makes them live longer than normal vertically is only when a smash down is input through some means while going upwards. Other than the result being some kind of downward movement or downward acceleration I don't know what else could explain what keeps you alive if it doesn't work without that when the other conditions are the same.
Also, why don't you try breaking your shield to do the tests? That way you can DI beforehand and not worry about SDIing in hitlag or moving around before being hit. Is there another better vertical move that sends straight up to use that isn't multihit like Zelda's U-Smash?