I'd be a bit disappointed if a mature system like FreeBSD contained this feedback loop in resource allocation

Oh, is the perlmonks server running FreeBSD? I didn't realize. In that case, top doesn't appear to show parent process IDs, unless I'm missing something. There are things I like about FreeBSD, but its version of top is not one of them. The ps that comes with FreeBSD is rather better, but in a scenario where you can't start a new process, top could be already running, and I don't know of a way to make ps do that (i.e., be already running and report output periodically).

I recall much older systems noticing a problem and selecting processes to be completely "swapped out"

I've observed on my desktop that FreeBSD will kill a process if it consumes too much RAM (in situations where Linux wouldn't, although Linux since circa 2.2 will also do this if the entire system is low on RAM, which is better than the Linux 2.0 behavior; but FreeBSD will kill a process for this even when there's unused swap space, if it surpasses some per-process memory usage quota). However, one process using lots of RAM is a very different scenario from many processes being spawned. I don't know what FreeBSD does with that. I could test that here with a forkbomb, I suppose...

Indeed, I don't have any access to /proc

That could make it hard to get a good look at the process tree.

So would a self-built 'top' on an unprivileged FreeBSD account be useful?

I don't know. It also seems like there _ought_ to be a tool designed to prepare a process ahead of time (preload it into RAM , go ahead and ask the operating system for a process table entry, and so forth) to be launched quickly, which might allow you to set up ps to run and then, when the problem is noticed, trigger it to go ahead. I do not, however, actually know of such a utility.

I feel your pain. Having to work around the lack of root access to accomplish things that would be much easier _with_ root access is certainly something that can be annoying. (I can also understand why the hosting company doesn't want to hand out root access, of course, but that doesn't make your situation any less frustrating.)