Shading is fantastic. I think though something that could help it is a shade from one color to another colour so it looks spunky. Like =LeoLeonardo's tackle emote.
I think maybe the shading could be slightly lighter too, but is probably not needed. If you decide not too, I think the outline could be slightly darker, but that's again my personal opinion.

I think the eyes are fine. If anything he darkening of the eyes could be a concern, as it almost seems as if it's being antialiased unless that's what intended. I still like it though. The highlights beneath his eyes are great; I really get the sense of depth and as though he has a nose.
Eyes, in my opinion though, can be a sign of one's style, but it really depends on the look you're trying to achieve. As you can see in my recent submissions, my emoticons' eyes change again every now and then. I just find it extremely annoying when you can't get that dramatic face across to the viewer without changing the main style of eyes.

But enough about me ranting on.

The animation is flawless. Fluid, smooth, squishy... all the elements you need to make a fantastic emote.

The new style, overall, fits perfectly for any emote. Just remember, you do not have to stick with this for every design you do: every now and then, drag in your old emote's shading for an animation.
Because this shading is so detailed and attractive, I personally think you should use this style for small animations or static. You don't want the overuse of 'drawing-to-attention' effect on the body in longer and more animation based animations.
But then again, it is your choice.

Great style, however, and I'll be looking forward to seeing this used in the next few emotes.
I use way too many words.