I'm not sure that's true. While you don't end up with lightspeed expansion, if you get to the point that you have the tech to live on an "iceball" by extracting

I'm not sure that's true. While you don't end up with lightspeed expansion, if you get to the point that you have the tech to live on an "iceball" by extracting the hydrogen and fusing it for energy, and can make the rest of what you need from raw atoms and energy, you can just sort of... keep expanding out into the oort cloud indefinitely, until after a while, you're not in the solar system anymore, and even more eventually, you're in another one. The more we learn the less empty interstellar space looks. That's certainly slow expansion, but it would be an expansion that in relatively short order would greatly exceed the biomass and biodiversity of Earth's biosphere, until it would be quite absurd that the whole thing would simultaneously decide to just stop one day. It would be slow but as difficult to stop as the biosphere is today. This does depend on some sort of practical fusion tech, though.