First of all, this is a phenomenal project. I never really noticed how shuffed the elementals get, but they certainly do.

As for the air, IMHO there could be something more thematically appropriate than "The Eye." I love the concept, but I don't personally feel like it fits well with an air elemental (although obviously its your homebrew and your choice). I have a theory as to why it's been difficult to come up with unique offensive prowess for it. With the other three, you were inspired by something connected to the threats the pose; you mentioned
a standard hit-stuff Earth elemental in the Mounder (though I'm considering making use of the ability to make difficult terrain and making it a lockdown AoO tripper), a grapplemonster in the Aquiform, and a variable-range poke/blaster in the Kindlewraith
So you have:
  • The Earth slamming you down, like landslides, or erupting unexpectedly (AoO) like the natural terrain being slippery and dangerous (or full of earthquakes)
  • The Water drowning someone because they're not strong enough to fight against it
  • The fire straight-up jumping out and blasting you (ever been close to a big bonfire?)

All the established powers are analogues to the inherent danger we associate with those elements of nature; but air is what we breathe, and the only natural disaster that tends to spring to mind is a tornado--hence their appearance as cyclone-like entities.

In my opinion, the best place to start is by identifying aspects of air that are deadly and terrifying. Off the top of my head:
  • The lack of air is a no-brainer; an adaptation of suffocation, strangulation or constriction could work here to do something along the lines of what dragonjek suggested
  • When there's something dangerous in the air: maybe implement poison use with the air elemental? This would also go well with the assassin-y feel
  • Strictly speaking with tornadoes and strong winds, they toss things around. A grapple build that throws people doesn't seem very fitting or effective, but maybe if the air elemental did bull rushes and charges it could illustrate this aspect

Those are my first impressions from scrolling through this thread. I really like what you've done so far!