Now that I'm not terribly busy with school, I was able to analyze my animation more. I took everything apart, especially the shoulders, which I isolated here:
The one on the left was the old shoulder. It's hard to tell, but there is to some degree a bit of an arch simulated here, its just heavily distorted by the up and down movement of my initial running animation. I made the path in more of a traditional arch like you mentioned, which not only makes the animation more fluid, it is also more accurate to how the shoulder moves in a running cycle.
From here I added the second shoulder and began reconstructing the torso. Originally the torso was static, but the pecs/upper chest actually moves with the shoulders. I blocked in where the weapon would be, and I noticed that the rifle would actually follow the same path that the pecs/upper chest was taking. I added some detail to the weapon, and added the arms back in:
Nothing in the legs was really changed, except for the back leg, which I darkened temporarily to make the legs more distinguishable:
I honestly don't see anything wrong with the legs, other than the fact that I need to clean up the pixel clusters in each frame. I'll add the up and down movement of the running cycle next, where the groin moves upwards and back down as you mentioned.
While looking at running cycles, I stumbled upon a few pixel animations where the head of the character moved along with the shoulders and pecs. I noticed that my character's head was static, so I attempted to implement something similar. However the head moves way to much for my liking. I'll probably have to experiment with the timing and or frames to tone down the head movement a bit.
By the way, I really appreciate all the feedback you've been giving me MysteryMeat.
I didn't think that your advice was unclear per say, it's good advice, and I understood what you meant. I just think you could have elaborated a bit more, no need to apologize for that though!