“seems that it was Newton’s reasoning that God was a God of order and that the universe could be investigated in an orderly manner to learn more about Him”
That was his reasoning, yes, but not his scientific reasoning. God stands without His own creation. Newtonian science is concerned only with creation. You don’t read “because God said so” at the end of each law of motion, and if you did it would be scientifically superfluous.
God is metaphysical; Newtonian physics is physical, naturally.
It seems Newton got his "non-scientific" reasoning from St. Thomas.
“. . . no opinion or belief is sent to man from God contrary to natural knowledge.”
. . . T. Aquinas, Of God and His Creatures , Book I, Chap. 7