Here are some quick notes. And I think it is fine to focus on feel without context to a degree - especially if you know it will be a game about platforming. There is something to say for making the simplest representation fun. You will approach the point where personality is going to start making a big difference, however.
- The jitter down slopes feels jarring when juxtaposed against the smoothness of the rest of it
- You should add back in some acceleration on the momentum – it is too hard to make small adjustments
- Automatically walking up the stairs is pretty rad. I’d suggest playing with a bit of a penalty with the momentum whenever he mantles up over a ledge (stairs or platform at the top of a jump). It might give the action a bit of substance.
- I know you are not working on the camera, but if you make it not blend upwards until the ground height below your feet changes, it will have a pretty big impact on how the jumping feels. You’ll feel the character’s weight a bit more when the world isn't vertically panning on lift off.
- I’d make the wall jump always push off the wall a bit. Without a neat climbing animation (or rolling up the wall animation if it stays a box), the upwards slide doesn't feel like the result of a physical push.
- The input feels a bit latent. I didn't time it, but I'm guessing that the rendering pipeline (e.g. post process) or the character logic (e.g. order of input tests, physics impulses, state transitions, and physics integration) is adding extra frames between button press and motion. With Unity, I doubt you can making it perfect, but even so I think there is something off.
- I see you already added in support for a late jump which is great. Another trick you can explore is helping the character decelerate a bit faster when approaching fall if the user isn't pushing towards the edge. This might not be necessary with some adjustments to the translational physics, but as is it is pretty easy to slide off stuff.
- Using an X360 gamepad:
- Jump is on the Y button. Unless you are making a statement (e.g. Ico’s up = triangle and down = X), I'd put it on A

- Analog stick input would go a long way. If you are against it, the input threshold that triggers movement is still too close to the dead zone (it might even be at the deadzone). I’d put it out a good ways.
- If you are sticking with the abstract box concept, you might also want to play with a little squash and stretch on jumps, lands, and acceleration. This will sell the momentum and help your brain buy into what is going on.
Hope something in there is of use!