So, again... those corporations aren't putting those people into power. They don't have that ability. They cannot buy the election of anyone. They can only buy attempts to influence the electorate.
Now, some of the stuff you suggest here is simply illegal, or minimally banned by the supposed code of ethics.
The answer to this stuff is to... simply not elect those people. But that's presumably impossible?
Look at Charlie Rangel, for instance... Somehow that guy is still in office. Not because the corporations which gave him mountains of money made it so.. but because people went out and voted for him to be there. The fault is on them, not on the corporations.
I understand why such things are necessary.. mainly because voters in the US are incredibly apathetic. But that's our own fault. You shouldn't need a GOTV effort to come and drag you to the polls. You should go to the polls because you actually care what's going on in your country.
Since people don't, all of the suggestions for "fixing" the system are pissing in the wind, because you're ignoring the fundamental issue at the core of everything... which is an uneducated and apathetic electorate.
When the voters can be won by tv commercials, then the election will be decided by who can run the most commercials. But that's not how it needs to be. It's just how it is. If the electorate were not so easily swayed by people jingling shiny objects in front of them, then much of this corporate influence would be expunged from the political scene.. and if the electorate cannot change, then frankly, we get what we deserve.