Thanks for giving it a shot. The axe kick definitely needs to be sped up and made bigger, it becomes active once you can see the foot come out about a third of a second into the animation. I think you are right that dying should just restart the level instead of kick you back to the menu, I will make a note to change it to that (i just got in the habit of pressing R/start as soon as I died to quick restart so it never occurred to me). Level 3 is the only level with a time requirement to unlock the next level.
Feedback is much appreciated