not sure if this'll work, but consider briefly taking the sphere after it's cleared out the adjacent planets. Once the ZPG and such flip control, immediately delete your orbital and then hopefully your power generator will remain under your control. After that, just make sure you have supply.
PS-make sure youve got something on hand to deal with any of the potentially hostile ships the dyson might spawn during your brief occupation. Ideally, you'd use an orbital 1 station, and speed build with multiple engineers to minimize your window of vulnerability (assuming it's hostile while you are building the orbital. I can't really say, since I havent had cause yet to capture a dyson).