Cool stuff! Those mockups/screenshots look great
Concerning the dorky run, the sword's wobblyness I think can be reduced by making the sword arm and sword static for 3 frames (frame 4 is nice), then tip up on the 4th, back to static 3 frames, tip down on the 8th. Also maybe hide the farthest arm completely on at least 1 frame on the backswing to imply more motion.
Try hyperextending the forward leg a bit on the step maybe? Though I think that would need a deeper running lean to compensate.
Did of couple edits of the attack for fun (they're sloppy but I hope they can get my points across)
First one played with the timing, added a doubleflip, and exagerated the downward cut motion. Also reused the crouch frame to stand back up at the end.
Second one is playing with the frame order for different effect.