Try this: http://adobe.ly/2gvBjMq
I had to reimport it so you might have to re-rig some sticks and a few other things. But:
a) You had all the different head groups (frontal, left profile, etc) tagged as "head" - you don't have to do this, you just need one head tag for the parent head group.
b) The biggest offenders were the head groups - note how the blue bounding box is a vertical rectangle instead of just surrounding the head. It looks like there was some leftover artwork or something in the head background layers that was messing up the shape of the mesh and causing warp issues. I deleted those and it seems to work better.
I checked the puppet you sent me and added it to a new scene. I can see that the head is better attached to the body but if I make any changes (even if I only toggle the eye icon or tag the eyes correctly) this happens: Bug Report.png - Google Drive and I have to undo in order to fix this (I can't just "untoggle" or "untag" whatever I did) :/
It looks like your spikes are all set to be independent? If you remove all the +s or crowns from them, I think you'll be fine (it should also help improve performance).