I was really envisioning less of a government forcing a population into re-population and more of a circumstance where people might find the programs appealing as in, "there are no jobs, but people can 'work' for the government by increasing the population in exchange for wages". I can see how repopulation might be less of an issue in a world with radical life extension, though I imagine that new problems would arise in such a society.Government programs to stop this will end in failure. The only way they could force people to reproduce is to control their lives with force - and that won't go down in a world with abundant energy (and a global brain).
Abundant energy = jobs completely redefined (i.e., you won't necessarily need a "job"). The early stages of a transition towards this type of new economy (which are still blurry), should be instituted with a universal basic income (UBI). Basically, we should have enough energy to make sure that no one goes without shelter, food, water, etc. This is possible now - if we had competent governments this would already be happening - but with abundant energy this would certainly happen. There are always problems. The point of this paper (as stated in the paper) is to identify the non-problems - one of the biggest being - overpopulation as a result of radical life extension."there are no jobs, but people can 'work' for the government by increasing the population in exchange for wages".
I can see how repopulation might be less of an issue in a world with radical life extension, though I imagine that new problems would arise in such a society.