Some form of "make the other command station harder to kill" mechanic would be good, whether temporary or permant, but please not an arbitrary invincibility.
I'm having a hard time thinking of such a mechanic that wouldn't either encourage double kills more or be able to be "cheesed around" (like more forcefields (penetrators, cloaked raid starships, etc))
Though that "AIP/time for each core guard post lost" is a pretty nifty idea, though it may need some refining to keep the game from spiraling out of control in the AI's favor if you aren't a fast player. Maybe adding some "AIP/some other trigger" for each core guard post lost?
EDIT: I would like to keep the AIP on AI home command station death, but reducing it some to only slightly above a normal command station and shifting the other "increases" elsewhere (either other units or other mechanics, or both), if for no other reason than the fact the the AI home command station is still a command station, and the AI should have some immediate, direct increase to their "dangerousness of the human scale" to their home being lost. (boosting both AIP and AIP floor would ensure that this would always happen, and splitting it between the two (not nessecarily evenly) would ensure that neither high or low AIP styles get off easy or are unfairly punished relatively)
And spawning a tough ship with a CSG effect on the other homeworld would be an great substitute for arbitrary invincibility.