We are not going to come up with a market-based solution to fix income inequality. The solution, as much as people in the dwindling middle class resist it, is a strong social safety net coupled with a hard reset on taxation and housing policies. Nobody should be homeless, nobody should be allowed to starve, but you might have to accept that your 401K goes down in exchange for a government guarantee of housing and food.
This is hard for people to accept because they currently have equity in their home or a 401K to save them from starving. But those are transient, individualistic solutions. You can lose your house. You can lose your 401K. Society should be taking care of each other in a broader way than letting everyone accumulate a little, private pile of money.