Here's why this makes sense: Chapter 2 was always a weak chapter, a grab-bag of stuff that didn't really fit anywhere else. It's also thin on documentation. And since chapter 1 is really a background chapter, chapter 2, with all its flaws, would be the first time that readers would encounter my work with the actual documents. And it's not good that this is the first impression they get.
Here's why I'm hesitant: this will leave me with a four-chapter book (not counting intro and conclusion), with those four chapters only totaling about 75,000 words. Add another 10,000 for the intro & conclusion, and another 4,000 or so for the bibliography, and that feels like barely a book at all. Plus, this seems like awfully late in the game to do a major rearrangement. It's like my version of a Hail Mary pass.
Yet, I'm about 80% sure I'm going to do it anyway.