OK, I now see what's going on specifically in my case. Definitely one of those stupid problems that I imagine there's no way Jenkins could account for it, so if I really care about fixing it I think I need to script a solution.
The root cause of the builds in question showing the epoch is that their build.xml does not have a <timestamp> element.
In our case, the reason is this: during a normal patch cycle, jenkins was yum-updated to a newer version, and the migration described in that wiki page happened correctly. Then, sometime after, puppet ran, and our puppet at that time was configured to pin jenkins to 1.596, and so it downgraded jenkins. This cycle probably repeated one or two times (we simply didn't realize it).
And so now, in each job's builds directory, we have a mix of old and new format build.xml files. All the symlinks are correct, but the busted builds do not have a <timestamp> element.
It's good to at least know exactly what happened.
Marc