Why only consider within-country inequality (and, yes, I realize that the answer is 'because it's partly a publicity stunt, and humans are biased and parochial')? The average American is incomparable wealthy compared to the average African, and you can on average save a life for only a few $thousand to one of Givewell's top recommended charities.
If there is an overpopulation of deer, we don't put big buckets of feed in the forest to support them. But for the human animal, that is exactly what we do.
I know this is a taboo subject, but I think that we may be creating more misery by giving charity, then by doing nothing.