Cheap Grace isn't an outcome of a moral system, it's a symptom of a lack of one.
Advances in psychology and neuroscience have provided insight into human morality. There are 6 moral foundations: (1) Care/Harm, (2) Fairness, (3) Loyalty, (4) Authority/Tradition, (5) Sanctity/Purity & (6) Liberty.
Conservatives place equal value on all six foundations. Progressives prioritize care/harm and ignore sanctity, authority and loyalty.
The current progressive moral vision has two priorities: tolerance and equity. Unfortunately, these are often diametrically opposed, which makes it difficult for progressives to articulate a coherent moral vision.