I'm glad it was useful! I'll try the game with the controller input and see how that goes.
- That crash showed "not responding" when I hit the button while in full-screen but not when the game was windowed, for some reason.
- "the inertia is necessary to make it impossible to climb walls" - technically not true! The typical way to do this is to make it so that the player has no air control for a brief period of time after wall-jumping (the game just moves them away from the wall), and then giving it back to the player after. In some games like Megaman X the time is brief and that lets you climb up walls. Other games tweak the timing so you can't climb. But the air control and inertia is independent of this, so you can tweak that however you like with this method.
- I checked out the playthrough "prettysober" did on Twitch that you linked. Honestly it did not inspire much confidence. :P He didn't get stuck on one level for 20 minutes like I did but he still struggled a lot, even with the earliest stages. Don't get me wrong, there's absolutely nothing wrong with making a hard game (hopefully it's hard in the good ways). But I would urge you to consider not using levels like these as your "tutorial." A tutorial should focus on explaining the mechanics, not testing your abilities (or your patience)-- that can come later!
- I'd suggest adding an explanation as part of your tutorial that sometimes the order in which you should kill enemies is not always what you might think at first. Sometimes level design can suggest things which the player make take at face-value rather than thinking of different approaches, unless you point out that thinking that way is a part of the game.
Here's another vid I made for you. Some problems here but it plays MUCH better with the gamepad!