I think that much of the problem could be unravelled with the creation of one new law. It would state, simply:

Corporations are not people and are not granted any protection by the Constitution.

The result of this clarification would be that corporations could no longer claim any right to free speech or privacy, and no protection against search or seizure. I have little fear of anybody being able to demonstrate that there is any likelyhood that corporations are human.

Stockholders (or at least the humans among them - think about that) would continue to have Constitional protection, but that is a far different thing. Employees would also have Constitutional protection.

I believe this change would greatly reduce the ability of corporations to influence elections or the actions of office-holders.