I'm happy to be proven wrong, but my understanding is that the atmosphere itself doesn't really care about "per capita", absolute numbers are what matters.

I'd imagine Vatican City has an even higher emission per capita than nearly anywhere else, but it would be silly to pretend that's where we should prioritize policy change.

As it stands, the one country produces more CO2 than the following 7 combined. That number is only set to increase. If our goal is a global reduction, should that not be where we focus the majority of our political energy? If Luxembourg went down to net 0 emissions, my understanding is effectively no difference would be made on a global scale.

The problem with your reasoning is that you think that the atmosphere problem is a problem that should be equally burdened by every country, whereas it should be equally burdened by every human. There is no reason that people that are inmore populated countries should be burdened more than people in less populated ones.

What if the more populated countries (ie: India and China) are the largest carbon emitters?

It doesn't have any effect on the logic. The limit of CO2 should be equal for every human being.