If what you're attacking isn't just money in politics, but the perception of money running politics, you can't content yourself with half-measures.
This strikes me as perverse. If the system is not corrupt but people believe that it is, the solution can't be to drive out corruption. It's not corrupt! And people will clearly believe it's corrupt irrespective of the reality.
I'm not sure what the solution here is - I'm not often impressed with civic education efforts - but tinkering with institutional rules to change perceptions strikes me as both risky and doomed.