Alright, so the first step is the expansion and consolidation phase. Spread to the whole universe, shut down the stars.
So, how to go fast. Antimatter is a definite possibility. It would be horribly inefficient to make, but if it lets you go faster than anything else, it would be used. The other one is spinning black holes to launch at very relativistic speeds. They spin in such a way that they drag space along with them even faster than light, and close flybys of a quiescent spinning black hole can launch you at relativistic speeds rather easily. I think I heard about a paper laying out a way to get arbitrary amounts of kinetic energy (as long as it is small relative to the hole) from multiple passes through a binary spinning black hole system, but I can’t find it and may have made up the whole thing. And you don’t need big spaceships. Remember, solid-state civilization, right? All you’d need is a Von Neumann replicator with some shielding from dust, some system to slow down from near lightspeed (it is very feasible to brake off the interstellar magnetic field), and maybe a big old antimatter payload in the back. Very small compared to the usual fare. So they’d be launching billions of these things in every possible direction as fast as physically possible, I’d bet >0.99 c conditional on not making that black hole thing up.
So that’s energy losses from things going over the cosmological horizon taken care of. What other energy losses are out there?
Gravitational radiation/background radiation. But it’s too wispy and evanescent to do anything about, and only really totals up to significant quantities in black hole or neutron star mergers, and it’s hard to do anything about that.
Neutrino radiation/background radiation: How the fuck do you catch and harness something that can traverse a light year of lead no problem? Can’t do shit about that.
The cosmic microwave background radiation? Well, to capture that, you’d need something colder than the void of empty space. Black holes would work as a heat sink, but to get it cold enough, you’d need a black hole the size of a planet or bigger, and you can’t enclose that in a solid shell, you’d need a dyson swarm. Also, I did the math, and the efficiency sucks balls on that strategy, you’d get a low enough amount of energy that it wouldn’t be worth it. Scrap that idea.
Dark matter self annihilation??? We’ll come back to that later. It’s too wispy and faint to practically harness now. Come back at the heat death of the universe.
Stellar radiation. Yes. Von Neumann replicator + asteroids/planets/comets = Dyson sphere on century timescales (exponential replication is a force to be reckoned with). Well, not sphere, more like a big toroidal swarm of very closely orbiting energy collectors. Anyways, the net effect is that the sun would go dark (though still probably radiate a good deal in the microwave part of the spectrum), and fuckloads of energy would get harnessed and piped into our cute little mini black holes for the cold dark end of the universe. Very important to get. (The net effect would be a perfectly spherical pitch-black bubble expanding at near-light speed, centered on where earth used to be. How’s that for your cosmic horror?)
Thermal radiation from planets and cold brown dwarfs and stuff. Yup, just establish a bunch of heat pumps (of whatever type) from as far down as you can get without melting, up to space. Cover the planet in heat pumps. Make most of the heat get caught. Freeze the planet to near absolute zero for long-term cold storage. Feed energy into black holes.
Stars inconveniently turning into widely-dispersed gas and dense useless remnants. Well... there’s some stuff to talk about later, but the main technology here is starlifting. In short, you take a bunch of the energy from the dyson swarm and feed it back into the star to make it expel matter. This is a slow-going process, operating at similar timescales as the star lifetime. So it would be kind of weird, seeing what happens to stellar evolution as the star gets less massive, and more and more metallic, with age, and the mass loss is dependent on luminosity. As long as you caught the star early enough (not sure what this means), the endpoint is likely to be a very odd white dwarf encircled by a dyson swarm, and a whole lot of hydrogen and helium scattered in a massive circumstellar disc for a second round of planet/brown dwarf formation. Now all this mass is in a convenient, retrievable, burnable form, instead of being locked in some fucking white dwarf core. God, what a waste that would be.
Dispersed hot gas: This part is actually really cool. Around 90% (number may or may not be accurate) of the non-dark-matter mass in a galaxy cluster is in the form of very thin, superhot gas. Why doesn’t the gas cool off and clump up to form stars (which can be blacked out and stored as fuel)? Well, this gas is being heated up. How? The supermassive black holes at the centers of galaxies. As soon as the gas starts cooling down a bit, it spirals into the black holes, firing them up again, heating up the gas. We want that gas cold and forming stars. The supermassive black holes will have to go. But how the fuck do you move a supermassive black hole? When spinning black holes merge, the gravitational radiation is asymmetric, and provides a “kick” to the black hole. A kick that can be thousands of kilometers per second. Under optimal conditions, a kick that can be formidable enough to launch the supermassive black hole clear out of the galaxy forever. So, sacrifice millions of stars (use dyson swarm to direct energy at one point on star surface, it erupts, star moves) to make a supermassive, fast-spinning black hole in an optimal configuration for launching. Wait for merger. Big badda boom, central black hole is out of the way, hot gas can now make many billions of new stars which are then quickly snapped up. Supermassive black hole removal: One of the key tasks for reconfiguring the universe into something better.
And that’s how you shut down the universe: black hole/antimatter-launched Von Neumann replicator => Dyson swarm => starlifting/mini black hole energy storage/star moving => make supermassive black hole => launch supermassive black hole out of galaxy => form 10x more stars to repeat the process.
Net products, going into the quintillion year sleep: A whole bunch of mini-black holes inside cold reversible computing nodes, a whole fucking hell of a lot of cold hydrogen planets, a dark matter halo, a bunch of white dwarfs slowly burning down, a bunch of frozen brown dwarfs, and a smattering of neutron stars and black holes.
Conspicuously missing: Supermassive black holes, interstellar gas.