It seems that with the inspector it is quite difficult to win mainly because his position can easily be determined and he can not change the identiy like the killer.
My proposal is: When the killer kills a innocent he may only access 3 adjacent cards which build a square of 4 cards with the victim to determine if the inspector is there. So at best the killer has 4 possibilities to do so. At an edge just 2. Then the killer needs more time to find the inspector which gives the inspector more time to get him. Maybe this could be integrated as a game option.
My proposal is: When the killer kills a innocent he may only access 3 adjacent cards which build a square of 4 cards with the victim to determine if the inspector is there. So at best the killer has 4 possibilities to do so. At an edge just 2. Then the killer needs more time to find the inspector which gives the inspector more time to get him. Maybe this could be integrated as a game option.