How are you using the Animator? I'd be tempted to use the Crossfade() method to directly change from one animation to the next and give yourself the ability to quickly cancel into another one if you need to.
Yep, that's exactly what I should be doing. Currently a lot of those animations are forced to complete before transitioning the player state, and it actually makes the controls feel sticky and unresponsive. It'll be a good fix for the post-jam version!