1) That's such awful reasoning. You're so set on the joint that your set-up forces it to be the most optimal play for the SK to win the game. 2/3s of your town is immune to NKs and whenever their BP gets popped, there's a jailer to protect them again, regardless of if the BP knows they got popped or not. SK basically gets a shot every other night unless he guesses accurately and finds a crumb. He could do well if he pairs with the Mafia but, again, that's the point: you're forcing him to joint in order to do anything at all or spend every other night doing nothing in an 8-man game. That's absurd.
2) This doubly ****s the SK then, because the Agent is effectively useless in finding the mafia.
Like, really, why have an SK at all at that point? Just have him be a second mafia with a strongman kill and be done with it.