What if it started asking you for stuff?
"Hey man, can I borrow a cup of energy?"
You build an energy reactor, it makes some more friendly gatlings.
"Hey, guys, um... can I have some of your scouts? I just wanna know what's going on out there."
You give it some scouts, it takes ownership and starts sending gatlings out to a few worlds further out where those scouts rest.
"Hey. Hey. Hey. Hey. Hey, you know that old golem you have there that you're not using? How much you want for it? Is it for sale? Aw, man, you're the coolest!"
After a bit, you see this souped up, but still really crappy golem, painted a primer gray, tearing across the different worlds, spewing smoke everywhere and generally just causing trouble, and there's this really trashy blonde in the passenger seat.
And occasionally it gets drunk or maybe a mysterious green cloud obscures it for a bit, and it wrecks a few of your worlds, no big whoop.
edit: Seriously though, I'm fine with the Dyson golem the way it is. Its downside in general is that it puts other planets on alert, which results in an increase AI buildup anyway. If you're going to make it even more capricious, make sure it's a toggle, or I may as well have it turned off.