Maybe have the gun be weaker, yes I know its a 1-hit in doctor who, but realistically that would be the most powerful gun in the game and even ERTs would be no match for someone who can aim. Otherwise it seems like a pretty good idea, you could also have a doctor who with a sonic screwdriver that can interact with stuff like a AI can and they have to convince the station to trust him to "close the blue-space anomaly" which is responsible for the Daleks.