Very nice!
Having the death button be the same as the restart button was a bit confusing though. I think they would be better separated. Alternatively, you could remove the death button altogether. As it stands, you never have to actually use it.
There's potential to design puzzles around a struggle to die, as the bodies pile up. Having the player ration out death locations in the physical world could be more intuitive than a finite number of respawns that changes every level.
Personally I didn't even notice there was a respawn counter until I tried to figure out why I was being sent back to the beginning of the level.