One could ponder whether it would make sense to use population control in addition to improved technology and development to make the ride across the world population peak smoother, to make the peak lower and happen earlier. There would almost certainly be at least some benefits to this, but given how long political debates about that would probably take, never mind implementing and enforcing the decisions, there might actually not be enough time to do this and get some noticeable impact out of it.
As long as it looks like the world population will peak around the end of the century, go for technology to make it as pleasant as possible, but if the outlook indicates that the world population does not peak or at least stabilize in the foreseeable future, then population control is really the only way or it will become pretty unpleasant as you indicated in your first scenario.
less desirable options: uncontrolled global civilisation collapse with rapid decline in living standards and population, nuclear war, etc
more desirable options: intentionally adjusting lifestyle / affluence in western countries, non-coercive methods of population control (e.g. better healthcare, increased access to family planning, increased opportunities for women to participate in education / economic activity, etc), less focus on short-term appropriation of wealth