I think simply looking at our socio-economic problems in terms of bare income is reductive. Income inequality is tolerable so long as people are sufficiently enabled and empowered in economic activity, and if they are sufficiently enfranchised through civic institutions and public services. For example, hypothetically there could be two societies, both with an average household income of 50K, and the top 1% being 100x that, but if one society has decent public healthcare affordable for the working class, and the other has brutally expensive, strictly private health insurance, there's going to be a significant difference in the life of the average citizen in one versus the other, even though they have the same income. Same thing goes with things like unions, employment protections, health regulations in the workforce, etc.
I'm inclined to think focusing on the building up of public services, and on labor regulations, will have a more significant long-term impact than simply fixating on income inequality.