In my view 'justify' is not appropriate here - 'develop a consensus as to the need for' is possibly closer to the truth. I do not believe it is sensible or possible to bring 'objective' evidence to bear on this question, absent value judgements. If we have a universal declaration of human rights then we have accepted that certain things hold for all human beings.
Climate change is a common concern of humanity.
Putting these together suggests to me that a value of life estimate needs to be constant across all individuals. It appears that the only acceptable solution may be to cite a range of values of life and cost estimates. I do however submit that to argue for non-uniform values of life on the basis of revealed preference is to use an abstract model to justify an empirical conclusion. This is not uncommon in economics but it is I believe an example of the fallacy of misplaced concreteness. I would be interested to know where discussion on values of life, which generated a lot of heat last year, has ended up.