Seems like a low risk approach for taking over a planet would be to just park a large shade between the planet and it's star then let it enter a deep freeze. Then you could just remove the shade and let the planet warm back up before settling down.
They can use that same technology to create, on a whim, inhabitable structures of arbitrary size and composition around any star- converting gas giants (or gas clouds or the solar winds) into perfectly positioned and constructed habitats in ideal locations.
Competition over planets would probably be as foreign and incomprehensible to them as what occurred in the universe prior to the Planck epoch is currently to us.