First, the Theistic Evolution book was not published by the DI.
Second, the DI includes a good number of people who are not “hardcore fundamentalists”, including Behe, Denton, Sternberg, Michael Flannery, John West, Bruce Chapman, Jay Richards, and others. Of these, none had an essay in the Theistic Evolution book, except West, and his essay did not advocate anything close to fundamentalism.
Regarding the article by Churchill and Murray, I share John Harshman’s disinclination to read it all. What I did read is mostly rehash of standard TE arguments. In particular, the “random events are compatible with divine providence” arguments have been around for decades, the ASA literature and BioLogos columns being filled with them. I didn’t find that Churchill and Murray added anything new of substance to those arguments, and I don’t find what they do offer persuasive.
They also seem prefer long abstract discussions of possible positions to discussion of examples. Instead of beating around the bush for pages trying to show that something might have a bit of ID and a bit of TE in it, why don’t they talk about authors who actually illustrate that combination? Denton and Behe both affirm universal common descent and design, but the article never looks at their proposals and teases out the design and the TE elements. A missed expository opportunity. I’m guessing these guys are professors somewhere, rather than professional writers, because they write inefficiently.