A confusing question, Joshua, in that of the writers on the Hump, only I and Penman bear the “Reformed” label (our corporate banner being “Classical Theism” - We include Methodists, Mennonites, Orthodox, Episcopalians, Baptists and even Jews. And Swedenborgians.), and only Eddie bears the label “ID” (though as I have said I find i have sympathy with some of their work).
Speaking then for myself alone, my reading of Calvin and other foundational Reformers does not stress special revelation at the expense of general revelation. Calvin regards the latter as bringing a basic knowledge of God to all men, and though he dismisses the possibility of a natural theology leading to a saving knowledge of God, even his dismissal of scholastic natural theology (ie the use of reason, rather than the observation of nature) does not preclude entirely the role of reason in general revelation.
Some of the Reformed English Puritans were very strong on the revelation of God’s glory in nature - one of my influences is the poet Thomas Traherne. Another George Herbert. If they were not more forthcoming on it, it’s because it was so general that nobody questioned it seriously.
I would see ID as seeking to redress a modern, and rather local, eclipse of general revelation: it is no coincidence that atheism is virtually unknown in primitive societies, or in European society until the Enlightenment. A properly basic (to use Alvin Palntinga’s parlance) awareness that God created all things, and created them well, has been masked by a combination of ideas.
I’d agree with them that the superficial plausibility of Darwinian natural selection - which seems to promise design free of cost - is one factor in that. That’s one reason I welcome the range of new discoveries in evolutionary science: the more the intuitively simple idea is shown not to be adequate to explain the reality, the more clearly our instinctive knowledge of God as Creator is restored.
As for the criticism that they are seeking to prove God by science, I disagree to the extent that they say it. However, it’s usually their critics who say that’s what they say: their own writings talk of things that are “best explained by a designing intelligence rather than by unguided natural processes” (a paraphrase, from memory). The goal is limited - to indicate external teleology. Any theological implications are limited to those of Reformed general revelation: “That God is the author of that teleology”. No ID writer that I know of believe in a natural theology that compares to special revelation on Scripture (even the non-Evangelical Moonies, Jews, and so on).
I should add that this is the kind of Natural Theology that B B Warfield, a first-generation theistic evolutionist and a Reformed Presbyterian, held. (Note that when I first discovered his writings, I identified myself for a while as a “Warfieldian Theistic Evolutionist”), He wrote:
“God’s revelation of Himself is ‘in divers manners.’” He lists a number of the sources of divine revelation, “Under the broad skirts of the term ‘revelation,’ every method of manifesting Himself which God uses in communicating knowledge of His being and attributes, may find shelter for itself – whether it be through those visible things of nature whereby His invisible things are clearly seen, or through the constitution of the human mind with its causal judgment indelibly stamped upon it, or through that voice of God that we call conscience, which proclaims His moral law within us, or through His providence in which He makes bare His arm for the government of the nations, or through the exercises of His grace, our experience under the tutelage of the Holy Ghost – or whether it be through the open visions of His prophets, the divinely-breathed pages of His written Word, the divine life of the Word Himself.”
Naturally he goes on to speak of the limitations of these for salvation. Just as he speaks of the limitations of Darwinian evolution!