I am continuing to enjoy, very much, your episodes on Peace. I think you are doing what may be the best first reading of Peace ever done. Unfortunately, Peace is to other Gene Wolfe books as Gene Wolfe books are to, well, ordinary books, in terms of the degree to which rereading unlocks its secrets.
So I recommend doing, at some point, a (possibly brief) rereading series, in which you consider the five chapters again. Maybe just one episode per chapter, with a bonus reread wrap up... I know, I know. Well, when I ever hit the lottery (to which I don't buy tickets) or discover I am Warren Buffet's heir (despite not being any relation to him & not knowing him), or even just get a big-time movie deal for Happenstance, I'll commission 'em.
If nothing else, you should find some way to deal with The Big Spoiler— the one that Brandon said he'd caught (I am guessing, even though he didn't name it). Maybe a section of one of the recap episodes that you could have first-time readers skip?
In the meantime, I have three brief comments on chapter three:
First, I disagree fairly strenuously with Glenn that Peace reads like a fix-up (to use that nettlesome term that has long outlived its welcome). I think the stories are so carefully thematically sculpted to relate to the narrative as a whole that it is simply hard to imagine that they were written separately. Yes, Wolfe did publish one of them in Gene Wolfe's Book of Days as "St. Brandon", but I think that seems clearly a retrospective excerpting.
An aside: I think that you mentioned the excerpting of Peace as "St. Brandon" in GWBoD, but did you mention that Wolfe said in an interview (see Wright, Shadows of the New Sun, p. 98), that "the St Brendan’s story in Peace is my version of an R. A. Lafferty story"? It seems worth noting.
Second, I know Brandon said he's supposed to be skipping the secondary literature until after finishing the book, but since he also admitted that he's not, I feel like I can share this non-spoilery tidbit from some bit of it (I believe from John Clute, although I don't have the reference & might be wrong): Clute (if it was he) noted that all of the stories in Peace are unfinished. Now, I'm not quite sure that's right; certainly some of them come to what seem a reasonable conclusion (the one about the porcelain pillow, for instance). But I thought of this because you noted that the main story in Chapter 3 sort of trailed off; it had an end, but it didn't resolve many of its plot threads. In that context it's worth noting just how many stories in Peace fail to end, and in how many different ways—the cut-off fairy tale in chapter one is only the most blatant fashion in which a story fails to conclude; there are others.
Finally, Brandon noted (and Glenn agreed) that the chapter got more sinister as it went along. I'm not sure I agree; I think the entire book has been incredibly sinister alm0st from the get-go. I believe in my comments on Chapter Two I chided you for underestimating the sinister element, Obviously you have now keyed in to the sinister element, but look for it in your promised Chapter 1-3 reread as you gear up to Chapter 4. I think the entire bloody book (pun only partly intended) is sinister; it drips from almost every page, without every coalescing. I don't think I'd say that it increases at all in Chapter 3; I think it's just there, as it was through most of it. Take a look; I think maybe you'll see what I mean.
I look forward to the Chapter 4 episodes, although I will probably hold off on listening to them until all the Chapter 4 episodes are posted—I think the Chapter 2 & 3 sets worked well as a batch, and so I'll do that again. (Anyway, since my comment on Chapter 2, to say nothing of my comment on the "Cues episode, is still under-appreciated (he whined), I'm sure you can all wait until then for me to share my thoughts. Grump, grump, grump.)
In all seriousness, great series & I look forward to the next. But watch for the sinister!