I'd suggest requiring everyone who submits a story to justify its relevance via the text box, ignoring all story submissions that don't have accompanying text (the exact opposite of how it currently works). That should deter a lot of impulse submissions, requiring users to think about why a story is worth posting here. And it should cultivate voting practices that maintain a stronger eye towards community relevance, as opposed to general interest. I.e., don't upvote unless the submitter successfully argues their case.
Restricting upvoting controls to a story's dedicated comments page would also deter impulse upvoting and force users to check out the justification.