With a long enough time horizon, the GP consideration ("If we continue to grow GDP (~energy consumption) at about 1%/y, we’ll boil oceans in 400 years.") will still come true even if expanding in space. A sphere expanding around earth at the speed of light grows quadratically in the outer boundary and cubically in volume, and will be overcome eventually by any exponent > 1.

I'm pretty convinced that increasing human activity so much to increase the background radiation to 373K is never going to happen, the point is more that any exponential energy growth eventually can't continue.

In a way though it's already happening, the GDP ~ energy consumption equivalence from the GP assumption does not hold (https://data.worldbank.org/indicator/EG.GDP.PUSE.KO.PP). We'll just keep inventing ways for the GDP number to keep growing exponentially in questionable ways for the system to keep going, until we can't anymore.