This sleepers idea is pretty cool. Is this a design document of your own, or something dating from one of the design iterations since the two Kickstarters?
I've been thinking of a somewhat similar idea since some people have expressed how scared they are of expanding and raising the AIP. It would be 100% beneficial to the player, not double-edged, so there's extra incentive to push your luck. You'd have AI warp relays that are all over the galaxy but that the AI doesn't bother activating until it starts sending exogalactic waves. Upon reaching the right AIP threshold they would activate all over the galaxy. Those pylons would be indestructible, and would be automatically captured by the faction owning the system. When the player holds one, he would get energy or some other benefit (big balance thinking to do here), perhaps scaling with the current AIP level. There would be no benefit for holding them for the AI or another faction - they're just part of the AI infrastructure.