In fairness, I seem to recall romantic envy/toxicity being a major part of their dynamic in the original 2007 Carnival of Carnage show. They've definitely moved away from the romantic element in all subsequent appearances, however, and it's safe to say they aren't presently exploring that idea anymore.
Haven't they been trying to do the "Eddie kills Jack" sketch since 2001? Do we know if this was just the mic'd Jack + Eddie performers trying to have some fun, or was it an authorized idea that fell apart? Either way, I don't have a lot of confidence that Eddie will be the icon next year.