It was a brutal struggle, and taking the hub planets was a pain in the butt, but I prevailed in the end! Wooot!
As you can see from the map picture, the AI was cutting a big swath right through my territory after the first AI world was destroyed. He literally swarmed me with Etherjets in order to bypass the key security worlds, and taking out the stations with Raid warships.
The P9 planet on the far right was the first homeworld, the marked one with all my ships on it was the second. I took them out with roughly half an hour inbetween. All in all, it took a little over 12 hours. Most of it was possible thanks to a friendly Dyson Sphere in the farthest left bottom corner. They sent me help that cleaned up enough for me to move through without too much losses, and still stay strong even as I approached the Core worlds.