So, I experimented with all of the "You Lose" screens (actually, I just died a lot) and several of them seem to be pointing to a previous level. I.E. dying (lots) on level 8 says "Level 7 Lost", or something to that effect.
This is nice and whimsical. The level design is great and movement feels tight. I can echo that sentiment about the spikes, they are hard to figure out at first. All in all, I had fun with this and I really enjoyed the variety of environments that you created from such simple assets. It all "clicked" really well.
The last level was a fun twist! I never know what to rate narrative on an arcade-y game, but this had enough variety in it that I think it fits the criteria.