My engine mounts are definitely toast (or at least very well-done bread), she shakes like a wet puppy on shutdown. I looked for radiator damage or signs of anything scraping, but I couldn't find any.
It's not a sharp increase in sound, it has some duration, like rrrrRRRRNNnnnh. Makes sense to me with bad motor mounts, like the torque of the fan is resisting motion 90° out of phase due to rotational momentum.

What's the diagnostic test for a bad fan clutch?

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RIP:
2011 E350 BlueTEC, Schwartz 81k (totaled by uninsured drunk driver)
1964 Unimog 404.1 (wrongfully towed by the city)
1994 E320, Brilliantsilber 208k (transmission shuffled off after sudden catastrophic fluid loss)
1982 300D, Silberblau under a blue repaint 256k (sold for parts)
1995 E320 Polarweiss, 131k (sold for parts)
1995 E300D Polarweiss, 287k (totaled by drunk driver)