None of the suggestions offered so far actually make the Dyson Sphere particularly compelling. "Boo hoo the AI was clobbered by the Dyson Sphere clearly I shouldn't have befriended it!" is... really not that interesting.
In my opinion, the best choice would be to remove the concept of friendly and enemy Dyson Gatlings. If there is a command station (AI or human) at the Dyson Gatling's planet, it does nothing. If there is no command station, then it spawns neutral gatlings, who then go around pillaging the countryside. Neutral gatlings would also be a bit different: they would be hostile only to the owner of the planet they are currently on, and friendly to everybody else. That way, they are a bit more predictable, less like the Devourer golem, and allow you to reasonably build a command station in the Dyson Golem's system.
The disadvantage is that, if they wander onto your turf, you have to deal with them. The advantage is that, if they wander onto the AI's turf, they have to deal with them. Fortunately, you also get to make the decision as to whether or not they're spawning. So, if the Dyson Golem is in the middle of AI territory, far from your borders? Free that sucker and have it soften up some systems, or at least divert (and destroy) some AI reinforcements. As your borders expand closer to it, however, the risk / reward becomes greater. The gatlings are softening up systems that you'll be taking soon, but they're also more likely to wander into systems you control.