Hi and thanks for your spirited critiques.
Thomas Paine was deeply involved with Illuminism--a branch of masonry--during his stay in France. This information is available in any standard biography. Was Hamilton a mason? I'll do some more research. In some cases, it's actually difficult to know for certain, since this was a quasi-secret society.
As to the Trinity, a marked change took place with the Masonic Constitution that Desaguliers authored. While the manuals of the older masonic craft guilds all made some reference to the Trinity, Desagulier's Constitution was silent on this point and never mentioned Christ. This does not imply that masons from that point forward were all non-Trinitarian, but that belief in a Trinity ceased to be a requirement for participation in the brotherhood. In its paragraph on "God and Religion," the Constitution enjoined newly minted masons to overcome theological differences to join in common moral endeavour: "But though in ancient times Masons were charg'd in every Country to be of the Religion of that Country of nation, whatever it was, yet 'tis now thought more expedient only to oblige them to that Religion in which all Men agree, leaving their particular Opinions to themselves, that is to be good Men and true, or Men of Honour and Honesty, by whatever Denomination or Persuasion they may be distinguished." The emphasis was on moral conduct and character rather than theological correctness. Since Desaguliers wrote this passage, I feel confident it reflects his own spiritual orientation.
My sources on freemasonry include Bernard Fay's "Revolution and Freemasonry 1680-1800" (Little, Brown & Co., Boston, 1935), and Margaret Jacob, "The Radical Enlightenment: Pantheists, Freemasons and Republicans" (George Allen & Unwin, London, 1981.
I stand by the overall accuracy of my description of freemasonry, its principles and adherents.