A constant growth rate requires exponential growth. Expansion into space is O(t^3) because you're limited by the speed of light in each of 3 spatial dimensions. Therefore, while expansion into space could buy us some more time, it's not a sustainable solution either.

I am not sure how this is relevant. Operate a large interstellar empire with slower than light space travel. The limits that article is alking about are there because Earth has its limits. Most of those limits are related to production of products and energy. If you could solve these outside of Earth (not even outside of the solar system) you are already in a much better position.