Final comment before I see some feedback from the experts.

I have this code in the worker function's loop:

    # quick pause to allow other stuff to happen a bit randomly
    t = 0.1 * random.random()
    time.sleep(t)

If I eliminate the sleep altogether pretty much all hell breaks loose.
As I reduce the sleep time it gets noisier and noisier.  I switched to
a fixed sleep time and reduced it as far as

    time.sleep(0.00015625)

At that point it was complaining about killing worker processes on
many of the runs, maybe 1 out of every 5 or 10 runs.

I suppose the moral of the story is to not use multiprocessing except
when you have long-running tasks.