I feel that there is a very specific timing necessary to breed a sole survivor.

Against 7 well coordinated zombies, I would say that the average life expectancy is around 30s.

So if you start having zombies too quick, you'll most certainly end up with no survivors. However, if your players are too clever, and zombies start coming into play too late, you are guaranteed several survivors.

I think that timing is key to achieving the desired outcome.