You assume economic growth is at most proportional to the rate at which we occupy previously unoccupied space.
That may be true, but it is not obvious to me.
My assumption is that all economic growth has some component that is based on matter and energy. Even if it's just firing of a neuron inside consumers head.
If that assumption holds, growth is limited by matter and energy. Assuming that you consume all matter and energy and leave behind maximum entropy (thermal radiation) the growth is limited by the area of an expanding sphere.
Light of speeds puts limit to the economic growth and it's less than exponential.
Maximum sustainable economic growth in infinite static flat universe is f(t)/dt where f(t) = 4/3×π×t^3.