As far as push/pull goes for verbal game, unless you're rolling in with a LOT of social proof or status, it won't really have a significant impact.
Push/Pull is extremely important when it comes to kino escalating because every other guy out there can't keep his grubby hands off her. So when you give her a big hug, throw her off, or if you guys are starting to get sexual, you be the first one to stop, etc etc. Don't be that next creeper dude.
It'll come with calibration, but I find that escalating to a K-close and going for the phone number is best way to deepen the interaction in my experience.
-Kevin