The Federalist papers are not law and therefore not binding. They are papers published in a newspaper by 3 authors (mostly by Hamilton). Certainly, there was no unanimity at the Constitutional Convention. So, given that only 3 authors’ views are represented, no solid basis exists for their sole use in interpreting the intent of the Constitution.
I’d like to put a sharper point on this. Nobody is arguing the Federalist Papers are law. They most certainly weren’t. And yes, there were several points of strong debate between the authors of the Constitution; impeachment was one of them. There were people who thought there should be a specific list of crimes, but this was messy and inflexible (abuse of power, for instance, isn’t something easily codified), so to was the idea of a trial in the Supreme Court. Hamilton may have been the author of 65, but there’s no reason to think that it wasn’t the consensus view of all involved; impeachment and removal of a President, a man who was selected by democratic process, was not a judicial decision. It was seen (wisely) as a political decision, and as such, the closest thing to a jury of the President’s peers was Congress. If it was a political question, then the politicians had to be the ones to sort it out. And because it was a monumental decision involving the removal of the President, conviction required a supermajority of 2/3s of Senators.
As to the division of the process between the House and the Senate, well that’s where Hamilton refers to Great Britain; because impeachment in British law saw the articles of impeachment voted on in the House of Commons, as the house of the people, whereas because in Britain you were dealing with the Crown’s own representatives and agents, the Peers of the Realm were the closest to being equals to the King, so the House of Lords held the trial (which fit well with the House of Lords being at the time functioning as the Supreme Court, through the Law Lords).
As to what Hamilton’s essay represents, well, quite simply, it represents the consensus view of the Framers. Even in 65, Hamilton does suggest there was debate over which body should have the competence to put the President on trial. Unless you have some reason to imagine that Federalist 65 is just Hamilton’s own views, if you’re a Constitutional originalist, how can you take any other position than it represents the intentions of the Framers as to removing the President?