Ross, I would not cut them down to a nub. They would most likely just regrow the same stem but why loose all the growth you already have? Just deleaf them and find somewhere to stash them.
I have seen some REALLY mature ensetes and never seen a pup on any of them. Not to say that they won't, but just not a reliable way to hope for a replacement plant.
By the way, I dig all the cat-in-the-banana pics you share
Our cat's love the bananas here too. It's almost as if it is taking them back to a place they belong or something.
Mike