In my own flat earth non-physical studies (which I enjoy far more than the sunsets, tides and Coriolis discussions that I no longer have any inclination to participate in), Newton always comes back to Deism and alchemy. These themes run so strongly through his work, and that links back to many other flat earth proponents ... Deism being a recurring theme in flat earth history. Deist symbols and imagery appear all over flat earth texts and art.
Many of Newton's friends were deists, and he finds himself at odds with his own beliefs and theirs, when he starts looking at gravity and motion of planets, which runs contrary to the Deist belief of a clockwork universe set in motion by God. He then can't square the circle. His gravity vs knowing there must be a creator. So he writes
This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent Being. [...] This Being governs all things, not as the soul of the world, but as Lord over all; and on account of his dominion he is wont to be called "Lord God" παντοκρατωρ [pantokratōr], or "Universal Ruler". [...] The Supreme God is a Being eternal, infinite, [and] absolutely perfect.
Opposition to godliness is atheism in profession and idolatry in practice. Atheism is so senseless and odious to mankind that it never had many professors.
He flip flops back and forth on so many issues leaving one wondering does he end up an ally or an enemy of the flat earth society? Its a lot like Einstein. Some of his theories are a problem, but then Special Relativity is needed by flat earth. Galileo, the same problems.
I shall look forward to reading your findings. I'll warn of my own experience though, on this forum. Not many people want to discuss such things. They always want to bring it back to sunsets, perspective or some equally dull similar topic so they can try to spring an 'aha!' moment on you, because they think no one but them could have mentioned it before.