At which point, the external SSD failed. Disk Utility was unable to resuscitate it.
Dear readers, you might think at this juncture, I gave up entirely and moved to the country to raise flowers and sob. But, instead, I was able to restore a clone of the SSD that had been made automatically the night before, reboot, and finally get back to business. (The drive is under warranty, and being sent back for replacement, after which point I hope to clone to it and resume my speedy external drive usage.)
Restarts will continue until morale improves
Do I have a moral of the story? You can see one: I should definitely get and be using more advanced disk diagnostic software, having had one to three drives fail on a system I use every day and then having what appears to be two entire interface types failing. Testing for faults also involves removing variables. When I first started having weirdness that I couldn't pin down on the system or software, I should have isolated drives, even though they exhibited no specific symptoms.
I should also be keeping my software up to date, but the 4.7.1 update of Default Folder came out only a day before I installed it, and I've been using 4.7.0 in Yosemite since it came out without problems. That wasn't the culprit, but it's a good thing to test for.
Unfortunately, I appear to have hit a blind spot in troubleshooting: without having any sign that a peripheral controller was failing, just odd pauses, there was no clear direction to move until an actual total failure occurred. All I know is that I'm deeply exhausted, mildly relieved, and throwing myself back into the breach again on your behalf.
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