Overpopulation

How should overpopulation be dealt with?

Natures natural adjustment mechanism is disease. But that is being interfered with. People are living longer than ever due to advancements in medicine so much so that it isn't sustainable anymore.

Nature doesn't have an adjustment mechanism, this implies it was engineered which is a philosophical matter and not a scientific one. If god (or allah, buddha, new age bullshit or whatever) exists then I am pretty sure they have created this universe for the express purpose of us being rational and using science to solve problems, or they would have not engineered it in such a manner as to suggest this, so for the sake of argument we should be investigating it's nature rather than it's creator. It appears human population is affected by an enormous array of factors and we have no one single totalizing theory that can explain it all, we can only identify various trends and look into the main causes to reduce the impact of overpopulation and this is what civilisations have been doing to some extent for 1000s of years.

Disease was omnipresent in medieval societies and famine had to occur before disease had an impact like the black death or the justinian plague, so while your initial observation is not wrong it does not explain everything, other factors include the inclination of poor couples to have large families, prohibitions and poor access to contraception aswell as factors that reduce the ability to supply the population such as drought, war or oppressive regimes using starvation to pacify a population. For the most part a malthusian catastrophe is an oversimplification, of course he did not factor in changes in technology but he also did not factor in the gradual decrease in the rate of increase of food and the varying levels of health in a community which results in increased death rates among the very young and very old as the food supply steadily decreases, however like your idea OP I also accept it as a small factor, a baby boom results in a youth bulge (imagine a population/age graph here) that gets hungrier as it gets older which is indeed yet another factor even if it is neutered by new food production technology.

So what is the most major factor? Technology of course, and the resources needed to utilise it aswell I suppose, sooner or later technological advancement will slow down and resources will be depleted making the opposing factors I've mentioned more and more noticeable which means society will have to focus on the allied factors.