Here's one idea I might use instead of the dome one. It's still the same basic concept though: a group of people get stuck in a small area and things get worse and worse as time goes on.
Basically, an alien ship crashes on Earth and the technology on board allows faster than light travel to be invented. But only months later, before real space travel operations can start, the aliens that sent the ship find it, and Earth gets taken over by transdimensional invaders who are technologically and physically superior. As the world's governments start to fall one by one, the UN puts together a starship crew made up of people from every country, and sends it into space with the hope of finding another habitable planet and rebuilding human society. But things won't be that easy because the crew doesn't know where to look for this planet, and there's other aliens who aren't friendly. Plus, supplies are finite, meaning that they have to be stolen from enemies or else the ship breaks down and everyone dies. There will also be missions against various enemies, both the ones that took over Earth and others who are hostile to humans, which I think would work similarly to the missions in the XCOM RP. I plan on the story endings varying wildly depending on what happens. If everyone collectively screws up with their choices, the starship will get destroyed. On the other hand, it would be possible to reclaim Earth with the right moves, or to find a new homeworld.
Do you seriously believe that I have the prowess to pull this off? 
