Not a postage stamp, but one that you push down to leave an imprint, right?

You could cover up or scrape off the "Mister", so it doesn't get stamped at all.
You could also make paper covers with cutouts that only let part of the stamp through, i.e. "Mister", "Jackoff person" and date get stamped separately, but you would have to align them properly each time.

Also considering the amount and frequency you have to stamp, ordering a new one might not be the worst.