What I did that got it to work was:
1) Carefully inspect each Homeworld to pick the one with a wormhole close to the AI Home Command Station.
2) Evaluate the Core Guardposts on that AI HW: Wrath Lance, Grav Reactor are BIG no-nos, for example.
3) Move most of the fleet to the core-world side of the close wormhole.
4) Send a small force is transports in through a different wormhole. This task force will immediately run away, drawing off the Reserves and as much else as possible. Radar Damping units are good here.
5) Send in your main force EXCLUDING the Blade and start heading towards the AI Home CS.
6) Shortly behind, send in the Blade, and tell it immediately to move at full speed to the destination. Don't let it stop for any reason.
If there is no wormhole close enough to the AI Home CS, or the only one that is also has Wraths, etc, then you'll need to do the CSGs first, then attack and clear some of the CGPs first. At least you can suicide attack that way, since you won't need to worry about reprisals (one way or another).
Despite all this, it still took me a bunch of tries. If the spawned Exowave included AI Riots, it was game over right there - they'd just push the Blade away.
I tried Warheads, but since there's a new spawn every 10 seconds, you basically need to expend an Armored Mk III on the AI Home CS every 10 seconds to keep it clear long enough.