Regarding direction of reform:
Reducing the discretionary power of the state would help, because the state would then be less able to discriminate and hence there would be less reward for power-seekers.
I suspect that strong federalism would help, by reducing the rewards for grabbing centralised power, and enabling instructive (and harder to control) diversity among more-local governments.
Forcibly de-merging (that is, splitting) large corporations would help, and wouldn't significantly impair market mechanisms (indeed, it would likely improve their operation).
A voting system that put the vote in the hands of people who had a more substantial incentive to pay attention would help. Today, an individual's vote has little chance of making a difference. There are systems that could correct this, while anchoring electoral power in the informed preferences of the general public.
Regarding the political power necessary to force reforms:
I have no idea, unless it is to make the internet a far more effective mechanism for truth-finding and deliberation. But that would require enlightened software development, perhaps as a result of one wealthy person with vision backing the effort. And this, in turn, would require enlightenment, which seems more difficult. Words and ideas I offer here may be used freely and without attribution.
Anything else?
Otherwise, I have to ask you to explain how our political systems fall short of democracy. tens of millions of people stand to see their lives ruined because the bureaucrats at the ECB don't understand introductory economics -- Dean Baker
If they don't I see no way to avoid the transformation to a plutocracy.