I'd be a bit disappointed if a mature system like FreeBSD contained this feedback loop in resource allocation. No system is perfect, but I'd come to expect better behavior when memory becomes scarce than such a feedback loop that makes the problem keep getting worse while trying to let each part continue to fight to do its thing such that nothing at all can get done and it takes so long before the system finally gives up and reboots (or is it that the system never gives up and pair.com notices the lock-up and eventually cycles power?). I recall much older systems noticing a problem and selecting processes to be completely "swapped out" (different from "paging", a more accurate term for what is often mislabeled "swapping") such that they stop fighting and other luckier processes get a chance to finish such that the resource exhaustion might pass or at least the system is capable of getting something done such that someone can "get in" in order to clean up "by hand". Note that when this happens to the 'A' web server, there is no hope of logging in to the system.
But perhaps this is just a case of bad tuning such that Apache fights too hard and it takes a while for FreeBSD to overcome it... Perhaps that is why many processes go to "0K" resident memory usage, though I'd expect a state much different than "RUN" to be reported for a swapped-out process. This lead me to notice again the angle brackets such as on "<httpd>" and searching "man top" for what those mean I find "COMMAND is the name of the command that the process is currently running (if the process is swapped out, this column is marked '<swapped>')" which isn't completely clear but somewhat supports that interpretation.
Since I don't have root access, I don't think trying to roll my own replacement for 'top' or 'sar' will be possible. At least, my assumption was that I'd not have access to what 'top' and 'ps' use to get all of that information about other processes. Indeed, I don't have any access to /proc (symlink to /root/proc and I have no access to even /root). But I see that neither 'top' nor 'ps' are set-UID nor set-GID so I'm not sure how the security is arranged. 'man ps' mentions needing procfs mounted (and referencing /proc and /dev/kmem). So would a self-built 'top' on an unprivileged FreeBSD account be useful? If not, I think just adding "ps" output to the existing "top" output would be one of the next steps.