While the advice in this post is all still quite correct – wholly independent backups are your only realistic hope of long-term data integrity – there’s an interesting quirk here that will be of interest to anyone trying to set up a large home storage array.
Finally, after all these failures, I split my storage array up into 3 pieces so that they'd be independent. But I was still experiencing an unusually high rate of physical device failure. Even as long ago as 2007, hard drives should be replaced at somewhere between 2% and 10% annually. So, if I had 10 drives, I should replace maybe 1 of them per year. But I was replacing them at a rate of maybe 60%-70% per year.
As a final hail mary, I went out and bought a UPS, and plugged all of the enclosures into it, and…
…I haven’t lost a single disk in the intervening 2 years.
After having a couple of months of good experience with this setup (i.e. after going for about 3x my previous mean time between failures with zero failures) I went back and looked at the numerous reviews on various JBOD enclosures. The bad reviews almost all list issues which are power-related; "turning off randomly" is highly correlated with data loss.
So my working hypothesis here is that most consumer-grade JBOD enclosures are simply not conditioning their power adequately to support hard disks, and require an external UPS to ensure even a baseline level of data integrity.