I don't think you can stop money affecting politics any more than you can stop piracy, or stop people from taking harmful drugs, or stop people from saying stupid things, or a lot of other things. In those cases I think the costs of stopping them outweigh the benefits. I just don't see any other way than constant vigilance.
You're absolutely correct that corporations/unions/organizations can and should be able to support positions, but that doesn't have to be a direct benefit to a candidate in that way that campaign contributions are.