Mafia as a whole is a game broken (for the purpose of consistency in competition) beyond repair. The meteor is a measure to reduce it, but it doesn't actually solve it due to scenarios like the one you listed. It works entirely through a sense of what's "sporting" and what's not-in this case, it's generally understood that the mafia will kill with the understanding that the doctor will be on the cop, as they can do so without losing, whereas in GAI it's understood that the mafia cannot kill or they will instantly lose (and thus will not do so). Yet, when meteor is on town in 4 way MyLo with 3 blues it's perfectly sporting not to kill-despite mafia not being in a position to lose if they do not do so.
My suggestion here would honestly be to always have meteor on mafia-sure it would mean mafia lose a lot of games they otherwise shouldn't, but it's the best way to get around the "sporting" problem.
So you're saying. Mafia could just NK in BV day 1. Keep hitting the cop and eventually doc has to just not save the cop after 3 days? That doesn't seem fair to town.