Think about harpooning a galaxy at, say, 100 megaparsecs, with a long rope attached to the harpoon. In the Milky Way, loop the rope around the rotor of an electric generator. In the distant galaxy, have the harpoon-end of the rope fall into its central supermassive black hole. Ignoring proper motions (the black hole and the electric generator are likely to move within their host galaxies, and their host galaxies within their galaxy cluster), this gives one about 72 kilometres per second per megaparsec of linear speed on the rope as the space between us and the distant galaxy increases.

Of course, you need a lot of rope, for the rope to be indestructible (and ideally of low mass), for lucky aim when harpooning, and for the harpoon to be able to carry rope all the way to the target, and for the target and far end of the rope to be impossible to separate.

The more local model for this is to erect a scaffolding well above an object in hydrostatic equilibrium (so anything from a round planet to a supermassive black hole) and fix electric generators to the scaffolding, driven by ropes dropping onto the scaffold-surrounded object. There are a lot of physics questions that can be explored using that model; it's a good exercise in all of them. (Some coursework uses this setting to explore the dominant energy condition of general relativity, since that imposes a maximum tensile strength on non-exotic matter rope or wire or filament: there is a speed limit on the operation of intermolecular/interatomic binding forces; c.f. Bell's rope-spaceship "paradox" in special relativity.)

> energy is not conserved

Carroll's point is that there is a generalization of conservation of energy in curved Lorentzian spacetimes, where changes in the motion of matter and changes in the spacetime geometry are exactly related. That applies in the harpoon-a-distant-galaxy model as well. The rope (and stresses within it) and power produced by the electric generator are all forms of moving matter, creating a geometrical change which (depending on the properties of the rope) may become non-negligible. A rope that is strong enough (and implicitly having much more mass per cm^3 than empty space) to connect two megaparsec+-separated galaxies (driving a generator at one end for appreciable time and feeding a black hole at the other for appreciable time) forces one into some calculating to answer the question: does the rope slow the metric expansion along its length?

Next, how do you get the generator to turn rather than be carried out of our galaxy? (We can sharpen this somewhat by dispensing with a generator, and throwing each end of our megaparsecs-long rope into a megaparsecs-separated galactic centre black hole. What happens if there is a large mass-ratio (heavy:light) between the black holes, or their surrounding galaxies? Does the lighter black hole get pulled out of its galaxy by the heavier? What happens as the mass ratio goes to 1?

Carroll's link above, showing \Nabla_{\mu}T^{\mu\nu} = 0 says that as long as we don't introduce further degrees of freedom we can calculate the equations of motion in the systems above. That is, it's fine for an expanding space with nonzero vacuum energy, and for that plus noninteracting (except by gravity) dusts. However, our very long rope cannot be non-interacting (it must be at least self-interacting) and its extra degrees of freedom are liable to become important under extreme tension (e.g., it might get hot and radiate a ~blackbody spectrum), so a somewhat different covariant equation would apply.