When I got my first sternum chin, I definitely used momentum to get up! By now, I can do it slowly for chins, but I still need momentum for the sternum pullup. When I am talking about 10 sternum chins in my last post - these are all done with momentum (feels like chest hitting bar rather than being pressed to it). Using momentum does not mean kipping - I just pull rather forcefully and "fly into the bar" instead of "grinding up" to it.
Your description of "pulling for the bar and 'pushing' my chest towards it" fits very well with what I do - pull and arch feel more like two separate actions to me - the arching part is not like a pose that I try to hold throughout the pull.