The lynch vote pretty much decides the game and who wins at that point then. Sure, we have a 50% chance at lynching the killer. But that also means we have a 50% chance of lynching the doctor, and if that happens then the killer can freely murder someone else during the night and make it a 1v1 and win.

Well, I guess it's a better plan than anything I could come up with though. Tbh I've been wrong about a lot of things so far during this game, so I'll trust your plan over my gut.