Liquid democracy is a proposed way to do a direct democracy in a large country. It's only been tried on very small scales (Google used it to decide which food to get for their cafeterias), so we don't really know if it would work, but I like the idea.

I'd point out that there are countries which don't have much corruption or governmental malfeasance. Nordic countries tend to score very well on the Corruption Perception Index, and also have good social safety nets and governments that (generally, for the most part) serve the people. They're all small countries, though -- I suspect that politics becomes an increasingly dirty business the more power a country has.

If you haven't already, you might want to look into selectorate theory. It essentially shows not only how the psychopaths at the top stay in power, but also why attempts to reform the system often result in a new crop of rulers who are just as bad or worse than those they replaced. (c.f. Cromwell's revolt, French Revolution, Russian Revolution). A proponent of selectorate theory would argue that the solution is not to remove the psychopaths -- it's to create a system where things in a politician's selfish interest happen to line up with things that benefit the people. It's excellently summed up by this video.

In terms of curtailing corporate power from the top down, studying the history of U.S. antitrust law would be a good place to start. Extra Credits has a good series about it.

One reform method that has worked before is unionization. The vast majority of worker protections came about because of labour action. Unions are a lot weaker than they used to be, but it doesn't have to stay that way. If you can, unionizing your workplace is probably the most impactful action you could take to improve the existing system.

If your tastes are more radical, you could also consider mutual aid societies. A robust one could conceivably Theseus its way into failing institutions, or evolve into a provisional government if everything collapses.