... its hard to do the between the legs portion due to its handle and just overall bulk.
I leaned from one of Anna's videos to rotate my wrist on the way down so that my wrist is almost turned 90 degrees in the back of my swing. This way the handle of the bell is in the narrower direction as it passes between your legs. I originally found it helpful to take some of the torque off my hand at the bottom of the swing as the bells got heavier. I use comp bells and later I used a friends cast bells and the handles were noticeable wider. That rotating definitely helped. Maybe Anna will comment on this.
I'm sure the difference in styles has been outlined elsewhere, but what would I need to do to go more hardstyle? The hip explosiveness?
@Anna C I think I understand what you mean by the "jump". I see what you mean by the legs coming forward, and I'm noticing a lot of "toes" in my upswing. This seems to be more of a jump, but should it be more rooted in the heels for this application? It seems like that would counter the legs coming forward.
I would recommend taming the arc a bit more (you are casting the KB from the top and have a fairly wide arc on the way up).
Personal Space Rules When Snatching the Kettlebell | StrongFirst