I'm not an expert on population dynamics but I'm fairly certain it doesn't work like this. The rate of population growth is going to be affected by the existing population numbers at some point, either because the area becomes resource-constrained and people start dying in higher numbers of starvation etc, or parents who are educated and have access to contraception see that opportunity for their potential children is more limited and they choose to have fewer of them.
Re 2, the deprivation account, that matches closely with my views except that most people also carry equality (of opportunity at least if not outcome) as a value. Almost no people hold only one ethical value at a time. Holding equality as a value is why people are disgusted by the idea of the utility monster under total utilitarianism, which is a single being that deprives more pleasure from a unit of resources than any other being, and therefore under total utilitarianism should ethically get all resources despite the misery this would cause everyone else. The same principle can be applied to your point 2. Extending the life of 8bn people who already have a relatively-large number of years to live is not as good as redistributing those years so that the people with the least get more, so that we end up with a better balance than we do now. I say this as someone who has relatively more to gain personally from life-extension than insecticide nets -- if you had to pick between giving a year of extra life to someone who is already expected to live to 60+ or to someone who will die at 5, egalitarianism would suggest that you should give the extra year to the child who will die at 5. If you have 35 years to distribute among a population of 35 people, one of whom is expected to die at 5, and 34 of whom are expected to live to 60+, it also makes sense to give all 35 years to one who would die at 5. This is true regardless of whether you believe in equality of opportunity or outcome, assuming you believe that the other 34 people have done nothing to "earn" their extra years as compared to the person with a life expectancy of 5, which I do and I think most reasonable people would.