There's little enforcement happening in those threads anyway—they're too free-form, and manual intervention is too expensive. But adding a rule should hopefully still make a difference.
Thats a lot of maybes, but my impression of the flag|vouch feature is as a first step community moderation and guessing it works well? The job thread being jobs targeting the community, I would think it would as well, or at a minimum help.
Obviously a company -actually- hiring the same kind of person month after month would be a false positive, but I thought it might help to catch some of these companies abusing "Who's Hiring"
At the end of the day the challenges likely stem from "Who's hiring?" being just a thread with comments on a very spartan message board. I would have said you can solve these issues with an app or website, but you already have one, so it would be easier to just leverage that and then the sky is the limit–add any features you want!