Police HVT Convoy: I've done this myself personally and have attended similar events like this in the past, but some kind of event where you would utilize all the cops (or majority) in a convoy with X amount of armored vehicles and X amount of normal vehicles going from point A on the map to point B. Their job is to protect the vehicle/person that the civs need to kill/kidnap/destroy. If the civs do so successfully then they and their group get an evenly shared reward of some monetary value. If the cops successfully push through all the onslaught they get some kind of monetary gain instead. The route would have to be very far and even potentially from point A to B and then back to A or to C just to make it a long enough event for multiple tries if needed. This could also be a scheduled event to some extent so there would be more than just one loosely gathered gang and a few randos attempting.
King of the Hill (Cop vs. Civ edition): A majority or all of the cops can participate in holding down a specific set of building or some area while the civs attempt to push it or vise versa. Either would be fun, but could both yield similar rewards to the convoy in terms of money and splitting it amongst the group who came out on top/won. This is something I've hosted many times as a trainer and it turns out to be really fun from both parties if hosted right with a proper location.