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Let's deal with the doctor-killers and the madman, and then we'll get back to the discussion. I don't think anyone will object, because this plan is preceded by eliminating the doctor-killers anyway.
And think about it, how does it look: in a game where most of it is based on deception, such a difficult task is proposed, which primarily depends on the honesty of one of the Mafia. Not to mention that, apart from one town member (let's assume you're a guard; I don't rule out either version), no one supports this "alliance."
Also, the madman is completely forgotten, who, according to the victory conditions, can win together with the town. Why is it excluded that, in the case of the doctor-killers being in a bad position, he will switch to the town's side? For him, this is the only right option, and in this case, the chance of "betrayal" is much lower than with the insane Mafia.
During the day, it is proposed to execute only the doctor-killers and the madman. Why not organize the execution of Hostor right now (based on his status and the priest's note, he can't be anyone other than an insane person), so that his comrades disrupt the execution and already lose half of their most dangerous ability, which, after the elimination of the doctor-killers and the madman, will be the main problem for the town and will lead to a "draw." If he turns out to be Radonar, even better, "let's equalize the town with the insane Mafia." And at night, let the insane people kill "the evil doctor, Torian." Whether they are in an alliance with the town or not, they are not fools and will not fail to kill members of a competing Mafia.
I'm not insisting, I'm just considering other options; it's unclear why there's such a focus on only one option.