There is no need to push if you are entering gathering cutting and releasing. Pushing to me implies Nage being "stuck" or resisting Uke's attack...at least (as Stenudd Sensei mentioned) that is the way we are taught in Shoji Nishio's Aikido.
An easy dynamic to see and "feel"... very very hard not to do...Thanks for the blog post.
When I find myself getting stuck... I personally switch back to a bokken to "remind" myself that I am an extension of the sword and to bring that "cutting flow" back into my technique.