(Emphasis added; all Biblical references are from the Amplified Bible)
Just curious... when was the "Amplified Bible" published? Did the authors of the DoI have at at hand in 1776?
Face it: your clips from Leviticus and Ephesians really have no relevance at all to the DoI. As for what the term "Nature's God" actually refers to, the most likely conclusion is that it was intentionally ambiguous.
The signers of the DoI were not of one mind when it came to religious beliefs -- far from it -- and this was simply a phrasal expression that would best lend itself to multiple interpretations, suiting the multiple (and incompatible) opinions about the supernatural held by the various members of the group.
The fact that the expression "Nature's God" never appeared as such in any English translation of the Bible (or any other religious text) was, I think, a key enabling factor in getting everyone there to agree that it was okay to use any kind of phrase referring to anything supernatural.
autotelicadj. (of an entity or event) having within itself the purpose of its existence or happening.