I can respect that, but you should know that it's equally unnatural to have your entire momentum ricochet in the opposite direction upon pushing the other direction button, which is how your game works right now. My original suggestion was twofold: 1) ground movement already responsively stops your momentum completely upon letting go of forward (even though both characters are running and would realistically slide forward a bit upon abruptly stopping), so duplicating that for midair movement would add congruency to the controls, and 2) you make the player jump on several one-tile-wide platforms in a row, thus making the player quickly push left/right alternating to avoid overshooting/slipping back instead of simply letting go of the button. This is annoying, not challenging.
You reference Mario 3, but that game merely slows you down at first upon holding backwards, thus eliminating the back/forth issue since you can just hold back for a bit to stop all momentum. Plus, Mario 3's ground movement also has momentum, meaning the player doesn't have to learn and instantly flip between two different movement physics within the same game. Even Super Metroid doesn't quite work the same as your game, because if you tap backwards quick enough, you kill your momentum and fall straight down (and even holding backwards, it takes a split second for you to actually move in the other direction).
By the way, both of your examples have run buttons, giving the player even more control over movement/momentum. Your game doesn't have a run button.
You want physics? You want momentum? Then COMMIT, because right now, your game's controls are much closer to all those indie games you take umbrage with than either of the two games you brought up to defend yourself.