I see it this way:
What practices have resulted in things being the way they are now? These practices are largely attributable to businesses whose policies are endorsed and enacted through government. Government politics are a complete morass and you've done an excellent job of painting how various parties might try and solve the problem.
So if government is a morass, how do you approach the problem? Certainly a career in politics is out of the question based on this presupposition. One might consider simply adapting how they act in their daily interactions with others. Personally I think this idea is too small-scale.
In my opinion, one strategy would be through the business side. Create a business whose policies create the type of change necessary for closing the gap between the mega-rich and "middle" class. The argument has been made in this thread that in order to compete, it is impossible to instate these types of policies. However, I believe this to be a false assumption. Certainly companies, even large ones, fall into a spectrum of "good" and "bad" practices. There appears to be no bound to either side. I take the David Deutschian view that any problem can be solved with the right knowledge¹. So the question is, can we think creatively, critically, and intelligently enough to solve this problem in business?
I believe the answer is yes.
¹ EDIT: Any problem whose solution is not explicitly prohibited by the nature of reality.