I appreciate the attempts Ubuntu people have made to reproduce the problem, and I'm baffled that myself and my users are still easily reproducing the problem.
I once again reproduced the problem on one of my Ubuntu configurations, and observed through "/proc/<pid>/limits" that the limits are "unlimited" on the process.
We have had multiple people reproduce this problem here, on multiple systems, at multiple sites, with fresh installs, on both i386 and amd64, and everyone saw the same erroneous behavior with Ubuntu packagings but not with upstream. Nor did Debian exhibit this problem. We have also been aware that the limit was in CPU seconds, not wall clock time. (I was very skeptical myself, when they first called me in as a fresh pair of eyes, after very experienced people there were stumped.)
I suppose the only thing to do at this point, as far as this bug report is concerned,are: (1) for me to start once again with a fresh Ubuntu install, and this time to carefully log each step in a form appropriate for this bug report (perhaps video it, too! :); and (2) for me to get the problematic Apache process debuggable and locate the erroneous behavior that way.
Realistically, this problem is so bizarre and has been so time-consuming that (though I wouldn't attribute "fault" til we know the cause), my users will also have to consider known-good options, such as running upstream Apache or switching the distro to Debian "stable" or RHEL/CentOS.