Here's easy and pretty optimized way to moonwalk to right: dash left, however don't make a full input that touches the controlstick frame, since that wastes valuable acceleration time. Then move the stick to the down right diagonal, and roll it to the full right input from there. Reaching the diagonal fast after dash to left registers is the most important part.
With falco you need additional momentum if you want to actually move backwards, usually from either wd, wl or walk.
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Goodin
The neutral position (in your picture the O) isn't actually relevant for avoiding turn. Turn is triggered if you smash input to opposite direction. So what you do is you move the stick to the x-coordinates just before the threshold of turn, and have the control stick stay there for 2 frames. Then when you on the 3rd frame (or later) pass the turn threshold, you no longer do a smash input, because you were close to the threshold. Conveniently the x-coordinates of the diagonal notches are just below turn threshold, so aiming at diagonal or little below diagonal pretty much guarantees no turn. As a side note it's completely possible to moonwalk going straight from left to right, it's just very difficult.