It seems to me that our desire for justice is basically a selfish desire for justification and often vengeance. Someone causes us pain so we want them to experience an equal share of pain in return. Or existential circumstances cause us to suffer, and we want 'justification' for it, even from God, as if our suffering is a 'wrong' that must be addressed in some way.
I find the insights of John Dominic Crossan to be most helpful here in regards to the ideas of justice. There are actually two types. Retributive Justice and Distributive Justice.
The idea of Retributive Justice is as you describe; paying back others for the wrongs they have done, exacting vengeance, and punishing them. The other Distributive Justice is about everyone getting the fair share of what is available to them. That type of Justice is about fairness for all, that the have-nots get to have the needs met, rather than the haves unjustly hoarding the pile for themselves.
Martin Luther King and his Civil Rights movement was all about Distributive Justice, that blacks could get to have their fair share of the benefits of social and economic resources, rather than it being denied to them by the majority white culture. We it about Retribuitive Justice, it would have not been a non-violent movment. It would have been about paying back the wrongs done to them to punish the whites.
In the Bible itself, you see both types of Justice on display. Different voices are expressing different views of God in these different types of ideas of what justice means. It's the same thing as you seen in our own society. Different groups of people with different views of what true justice means.
But the expectation that we should not ever have to suffer, or forgive those that cause us to suffer seems selfish to me. Not divine at all.
Divine justice in my view is Distributive Justice. "But let justice roll down like waters, and righteousness like an ever-flowing stream." Divine waters flow freely to all, not just to those at the top who control the spigot and sell it to others for personal profit.