Took some work but I finally got it in there. I'm really seeing the benefits of working with the Cut Out Animation style. Done with enough finesse and its not as obvious as you'd think. I added more arm and leg shapes and figured out a stopping animation that I like. Triggering the animation to happen on the button release instead of the player stopping fixed some previous problems that I was having. Now I just have to hand animate the cape and I'm good.
After this, I'm eager to move onto some flying animations.