I think the arm is coming way too far forward. He'd throw off his aim as well as his balance. Don't try things out on a treadmill, try them out on real ground. You can't train for a boxing match just by hitting a bag all day, and if I can run around a bed-stuy block with one arm out without getting jumped, you can too

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If he is going to flail like a madman, he can't keep his aim up like that. when one shoulder comes forward the other hangs back. that's not just a fact - it's the whole point of moving your upper body while running. It builds momentum and it keeps the body moving in a straighter line.
For the gliding issue, i see 2 things : there's no weight, and everything is completely even. I agree that you can't change the placement of the foot on the ground during contact, but you haven't attempted to change the placement of the body over the foot. Even Olympic sprinters who spend 99% of their time in the air still don't float.
The same goes for the doctor - he's a floating torso with the leg motion just for show. I get the feeling that you're animating these all as separate pieces and then wondering why they don't work as a unit. He's not only rigid, he's stunningly stable - more than is humanly possible. what's worse is that when you start this way, now when you try to animate the body to compensate, it will only look bad, because the animation wasn't part of the action considered from the beginning.
It's all a matter of process. Bad process leads to bad results no matter how much work is done and no matter how many problems are addressed. Always start, work, and finish with the whole advancing in front of the parts.