What a private citizen can do is NOT the problem
That's nonsense and a complete lack of understanding of the problem.
What a private citizen can do is the very root of the issue.
The 1st Amendment gives people the right to assemble, and that includes assembly in corporate form. In fact, the entire case that brought this about was little tiny Citizens United, a small handful of people with the same beliefs that wanted to make a political statement.
I won't proclaim to know the solution, but it's no where even close to simply saying private citizens can be treated differently from corporations, or "get money out of politics", or any other easy line to just toss out.
Maybe amending the 1st amendment to prevent assembly in corporate form (but I'm no lawyer, so I don't know if even that would work).