I like that you use the word "quirky". I wanted to use that word my self, but i didnt think about it earlier:) you are right about both the secund high point and the fact that he isnt in the air at any point. That is going to be my next goal!
If this thing ever becomes a game the kindergarden teacher could "transform" in to the astronaut in some storytelling mode. I would like to illustrate what working with children takes and what a healty fantasy can do in this inviroment.
Edit:
I tried to work on the run cycle for the astronaut. i cant get my head around peaking at the right places.. the legs is still rough, but this is more of a "is this better?" thing..

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i think that the breathing i have tried to put in to the animation is giving the impression that he is peaking at one point and not the other, but he is highest when he is in mid air.