Against advice from several people here, I decided to go with dowels to attach the (many) "rungs" on the sides of my cookbook shelves.
After turning the idea around in my head during the workweek, I modified my jig a bit. It worked very well. I drilled all of the holes (32 rungs x 4 holes) in about a half hour. This video (prettied up a little, courtesy of my daughter) shows me finishing one piece in a little under a minute:
That was actually the first attempt; I got a little quicker at it after some practice.
I had originally considered flipping the piece over end over end rather than rotating it; I could have used the same "fence" for both ends of the piece that way. But there would be a problem if the holes weren't precisely centered vertically. I figured they wouldn't be, so I needed a new strategy.
I decided to use two fences, one for drilling each end of the rungs. That way I could keep the same reference face. I decided it didn't matter if the holes were centered horizontally, which allowed me to use the edges of the drill guide as reference points.
As I started each new piece, I chose the "better" face and faced it downwards. I did the same with the stiles that mate with the rungs. That way the more visible face of each ladder should be well aligned. As it turned out, the alignment seems pretty good even on the other side.
I shot a quick video of how I drilled the holes in the stiles, but my editing staff has gone out for the afternoon. You'll have to wait. In short, I remade the jig to drill into the edge of the long pieces rather than the ends.