Sorry, no. It doesn’t work.
Creating a fictional dark political scenario like Dr. Strangelove is one thing: it’s comedic value is possible precisely because it is not based on history. Taking an evil historical figure like Stalin, who was responsible for the deaths of 9,000,000 people and making it a dark comedy is just offensive. Case in point: Beria has his security guard prep an underage girl whom he has already raped, groomed for a repeat offense. Question: can you make a dark comedy about Hitler in which people are murdered and raped and make light of it?
Some things just aren’t that funny.