I like the anonymity idea! That's a new one to me. It goes along with what I said earlier about politicians/people being polarizing and would move politics back towards policies.
As a registered Libertarian, I'm obviously also a fan of third parties. I see the biggest problem being winner-take-all elections, where 10%, 20%, or even 40% of the vote means 0% of the seats. This discourages moderate third party candidates from running. I think a better system would award seats proportionally to the votes won. That requires multi-member districts, so you can't do that for the presidency, but it would work for Congress, and I think you'd see the two huge parties break up into smaller, less powerful, less corporatist, and more ideologically consistent parties.
For the economy, I agree that wealth redistribution to try and achieve equality of outcome is undesirable. We need strong incentives to excel, and taxing the rich would be the opposite of that. This is why I think the main problem is just how easy it is for wealthy elites to translate their economic power into political power via campaign contributions, and why I think the solution is publicly funded campaigns.