That's a great idea! They are crazy about chopped greens in water, too, so I could possibly sneak in some fresh leaves there. I am growing some of the stronger Greek oregano that is used to make oregano oil.
My ducks could not stand any oregano oil in their feed or water, even in tiny amounts. They took one whiff and backed off! ( I take it myself, but for that matter I can't stand it either, so I put drops of it in gel caps so I can get it down...) I would think a prepared feed containing oregano...