I think one thing you say above is a key point:
in theory, anybody can form a corporation and operate it to take advantage of the extra "rights" to be gained thereby,
I don't believe a corporation should have "extra" rights. I think should they have all the rights of the people that make them up, and that's where it ends. I agree completely that there is a massive problem with how we treat corporate entities--whenever someone can, say, commit a felony resulting in the deaths, and some limited liability entity walks away with a token fine as a result, there is something seriously wrong... but your proposed solution doesn't correct that! We need to overhaul the courts, not restrict free speech.
How would restricting the political activities of that entity-in-law have in any way affected the Constitutional rights of the people operating it?
How does, say, the New York Times corporation operate in an environment where corporate entities do not have free speech and freedom of the press? You can argue that the individual reporters are simply exercising their own rights, but that fails once you dig into it--the corporation's money is being spent to give those reporters a voice. The editorial page is more than just the editor's personal opinion, it's the de facto position of the newspaper. "Vote for Giant Douche! He's better than Turd Sandwich!" is being broadcast to millions of people, and it's a corporation that's doing it.
How, possibly, can you deny this right and still be faithful to the spirit of the first amendment?