If you're far enough in that they are sending almost all core ships, then you're definitely in real trouble; how high is your AI Progress? It sounds like you've been steamrolling through every planet, but that's
generally not the goal.
It doesn't sound like your game is broken -- it sounds like you've lost. Certainly there are some people (Kalzarius, etc) who have successfully done conquer-everything strategies on certain maps, but that takes a really long amount of game time and is always a real grind, and requires strategies outside the norm. It can be done, and if that's fun for you then go for it.
But, if not, you might find this post on
the three phases of the game to be helpful in choosing a strategy in future campaigns that doesn't back you into this particular corner. If you get the AI Progress high enough, the AI is meant to kill you, and it sounds like the only thing that is keeping that from happening in the current map is that you've got an amazing bottleneck at the end of your snakes chain.
Not the best news, I know, but hopefully that helps!