Thanks for looking at this.
I am a bit redfaced right now, because it looks like I have to withdraw the question. When I used "bat" to view the Jobs Run, and clicked "Filter Copy Jobs", a lot of the confusing stuff was removed, and I could see that the dates actually had a monotonically increasing progression. Which means that, in fact, I wasn't getting duplicate jobs copied and the ones I thought hadn't been copied actually were.