Finally got it!
I mentioned before that the H/K Factory was acting wonky? I've finally got a save where it happens almost every time.
Edit:
Added a Mantis report.In the attached save game, do the following steps:
1) Load the game.
2) Pause immediately upon load - before the "X massive ships enroute to your planets" message appears. The game time should be 27:18:34.
3) Switch to the starmap. Do not switch to any other systems; leave the human Homeworld selected.
4) Switch back to the planet view.
5) Let the game run.
6) Sometime in the next 90 seconds, the AI homeworld way off to the right will active its H/K Factory and suddenly there will be a new H/K Mk I enroute.
7) If you hit time 27:20:00 without it happenening, reload from the beginning and try again.
The actual time the H/K spawns is random - it's been within a few seconds of the load, and it's been more than 5 minutes after. But 90% of the time, it'll happen in the first 90 seconds after load. I've included a log file that shows some of the times it has happened.
It happens even if I shut down AI War and reload, or reboot my PC.