They should try to execute him during the day and infect the town at night.
And considering that it's quite easy to get into a situation in the game with a Gunslinger (or rather, with two Gunslingers, one of whom only kills Mafia members, which means he doesn't have to worry about making a mistake) and a Doctor, where only Shabnak is left of the Mafia, I would advise the Mafia to save the Doctor even if the Prophet and Albino are still alive.
This leads to the question: isn't it too much to give the Doctor such forced support from the Mafia, in addition to all his other advantages?
Added 17 minutes later
Also, the Mafia should think before stealing the ultimate ability, as the Imposter's hypnosis is displayed in the newspaper along with the target's nickname.
The effectiveness of the Plague's actions is somewhat overestimated - until the third night, there are 5 roles for whom infection doesn't matter, then 4, but Clara will be able to heal and cure the Commander, as she will be with him.
Знание некоторых закономерностей освобождает от изучения многих фактов.
Мечты сбываются рано или поздно, так или иначе.