Providing a content-neutral system to reduce money in politics is possible. We know this for sure based on what happened after that Supreme Court decision Citizens United.

You'd enjoy Hugo Black's dissent in Connecticut General Life Insurance Co. v. Johnson from 1938, as the pattern of usurpation (via corporate standing in the law making process) goes back to the late 1800's;

I do not believe the word "person" in the Fourteenth Amendment includes corporations. "The doctrine of stare decisis, however appropriate and even necessary at times, has only a limited application in the field of constitutional law." [Footnote 9] This Court has many times changed its interpretations of the Constitution when the conclusion was reached that an improper construction had been adopted. [Footnote 10] Only recently, the case of West Coast Hotel Company v. Parrish, 300 U. S. 379, expressly overruled a previous interpretation of the Fourteenth Amendment which had long blocked state minimum wage legislation. When a statute is declared by this Court to be unconstitutional, the decision, until reversed, stands as a barrier against the adoption of similar legislation. A constitutional interpretation that is wrong should not stand. I believe this Court should now overrule previous decisions which interpreted the Fourteenth Amendment to include corporations.

Neither the history nor the language of the Fourteenth Amendment justifies the belief that corporations are included within its protection. The historical purpose of the Fourteenth Amendment was clearly set forth when first considered by this Court in the Slaughter House Cases, 16 Wall. 36, decided April, 1873 -- less than five years after the proclamation of its adoption. Mr. Justice Miller, speaking for the Court, said:

"Among the first acts of legislation adopted by several of the States in the legislative bodies which claimed to be in their normal relations with the Federal government were laws which imposed upon the colored race onerous disabilities and burdens and curtailed their rights in the pursuit of life, liberty, and property to such an extent that their freedom was of little value, while they had lost the protection which they had received from their former owners from motives both of interest and humanity. . . ."

"These circumstances, whatever of falsehood or misconception may have been mingled with their presentation, forced . . . the conviction that something more was necessary in the way of constitutional protection to the unfortunate race who had suffered so much. [Congressional leaders] accordingly passed through Congress the proposition for the fourteenth amendment, and . . . declined to treat as restored to their full participation in the government of the Union the States which had been in insurrection until they ratified that article by a formal vote of their legislative bodies."

Certainly, when the Fourteenth Amendment was submitted for approval, the people were not told that the states of the South were to be denied their normal relationship with the Federal Government unless they ratified an amendment granting new and revolutionary rights to corporations. This Court, when the Slaughter House Cases were decided in 1873, had apparently discovered no such purpose. The records of the time can be searched in vain for evidence that this amendment was adopted for the benefit of corporations. It is true that, in 1882, twelve years after its adoption and ten years after the Slaughter House Cases, supra, an argument was made in this Court that a journal of the joint Congressional Committee which framed the amendment, secret and undisclosed up to that date, indicated the committee's desire to protect corporations by the use of the word "person." [Footnote 11] Four years later, in 1886, this Court, in the case of Santa Clara County v. Southern Pacific Railroad, 118 U. S. 394, decided for the first time that the word "person" in the amendment did, in some instances, include corporations. A secret purpose on the part of the members of the committee, even if such be the fact, however, would not be sufficient to justify any such construction. The history of the amendment proves that the people were told that its purpose was to protect weak and helpless human beings, and were not told that it was intended to remove corporations in any fashion from the control of state governments. The Fourteenth Amendment followed the freedom of a race from slavery. Justice Swayne said in the Slaughter Houses Cases, supra, that: "By any person' was meant all persons within the jurisdiction of the State. No distinction is intimated on account of race or color." Corporations have neither race nor color. He knew the amendment was intended to protect the life, liberty, and property of human beings.

The language of the amendment itself does not support the theory that it was passed for the benefit of corporations.

https://supreme.justia.com/cases/federal/us/303/77/case.html

I'm sure Justice Black would not be very pleased with Buckley v Valeo in 1978, or Citizens United.

Then again, What Madison was talking about in Federalist no.10 (which I was copying in form for my OP, hoping someone noticed hehe) was not so much how the Union can use electioneering processes to safeguard the Republic from the influence of monied faction, but rather how the system of governance in America could provide a structural check on the behavior by virtue of the varied parties (in his time), and the "honor of elected representatives". Sadly, neither of these really came to pass, therein representing the core breakdown of our system of governance and, therefore, allowing for the corporate usurpation of our Republic via the 14th amendment.

Its really all quite sad in context, as this Republic was a beautiful thing.