I... Wow. That Bully homeworld should swap
this in for its background planet texture, with 6-sided dice instead of eyes.
As for what to do... if taking that black widow didn't mean permanently alerting 2 core worlds, I'd say go for it. Though I guess a warp jammer would help there. But remember that trick with "stealing" enemy ships out of a threatball with Riot-Tractors + Shield Bearers? The Black Widow is the Grand Matron of that trick (particularly with the paralysis tractors).
But that doesn't deal with the fact that if your AIP gets to any kind of significant level, a 3x core-raid-engine trigger... game over. Even if you had a decent whipping-boy, probably, and as you pointed out establishing one would just mean a ton more AIP.
Hive golems wield a fairly frightening amount of firepower, but the wasps accord not well with AI Eyes.
That Arty golem is probably a necessity for rapidly dealing with the key structures; can it hit the blue homeworld AI Eye currently? I forget if it has enough firepower to take it down without taking the guard posts down.
In theory I'd go with:
1) Grab black widow (with warp jammer), use it to free and nerf either the north or northeast from the blue homeworld, whichever seems less painful.
2) Using black widow, use it to free and threat-clear blue homeworld. Hope your AIP is low enough and your Cheese is high enough through this process to survive the raid engines.
3) Grab arty, use it to put out the blue homeworld's Eye, pull back from raid engine range.
4) Grab one or both Hive Golems, get them to max capacity.
5) Clear the CSG network.
6) Use the arty plus all necessary support (hive wasps will probably help a lot) to one-by-one the core raid engines on the blue homeworld.
7) Take all the golems and everything you can spare to smash the blue homeworld.
But my guess is that would go horribly wrong at the first mention of "core raid engine"
And depending on your thoroughness in threat clearing and the strength of your mobile offensive fleet, the hives may not be necessary. But they could be good clutch defenders, too, because I rather doubt that AI's going down without going for the throat.