I really enjoy the concept
1. It's somewhat hard to tell when you're on the wall or not. The light on the walls help but if there was a binary thing of are you on the wall or not it might be easier to tell
2. This might be different from how you intended the game to be played (just judging from your description) but I found that the easiest way to beat the levels was not to run along the walls but instead to jump into one, then while you're on the side of that wall jump again to jump on top of the wall. Then jump to the next one and repeat.
I actually found this really fun, and my only complaint is that I wish jumping was more of an automatic-style (hold space to continually jump) type thing rather than having to hit the space bar every jump. This also kind of combines with #1 because you can't tell if it's time to jump yet or not.
Very interesting though, I can't wait to play more :)