Well, My coolest drive (RED) runs about 95F and the other 2 run about 116-118f so your drives are plenty cool and my cpu runs about 36-38 so yours is better as well.

So, your temps are good, your drives are good.
I'm going with Power supply, plugged up/fan stopped/or dieing.
The power supply was the first thing to go on my 470 then the seagate main drive was next. You have done everything you can without gettin geeky...
The chances of a reload fixing it are slim, but that's about all that is left that someone without tools could do. Lots of people have taken them apart, but most of them are comfortable doing so. If you do a recovery (not Reset) make sure your important stuff is backed up
I'm at a loss now to what else you could do..

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[X510 CPU/RAM/All 2 TB Red's] [X510 CPU/Sync'ed Backup/All 2 TB Hitachi's]
[X510 /2 in box]
[X710 LIAN LI DIY W2016E] Stablebit Drivepool [EX-503 LIAN LI 5-bay USB3 External]
Fear the Cloud

Wait a minute!
If all the temps are Celsius not Fahrenheit
Usually around 50c to 60c is the limit on drives and cpus
If that is true.
Then the only fan workig correctly is the one in the psu/cpu area
Looking at the right column only
12:53
Drive 0: 37, ("worst" column: 65) Looks bad
Drive 1: 36 (67) Looks bad
Drive 2: 36 (71) looks bad
Drive 3: 38 (76) looks bad
CPU: 29 Looks good

So the cpu seems to be okay
I would suspect the two main fans in the rear.

_________________
VGA/PS2 Keyboard/PS2 Mouse/Serial debug board
Popcorn C-200
Popcorn A-200
Dune HD Connect
Rasberry PI OSMC(KODI)
ReadyNAS RN316
Amazon FireStick
Amazon ECHO
AnyDvD
MyMovies

But the "worst" temps seem to predate my setting the fan to run constantly at the highest speed. Along these lines, do any members of this forum live in or near New York City and have (or know of someone in the area who has) the tech computer knowledge to open up an EX475 and install a new power supply and/or new fans (I would pay of course)? I really don't trust myself to wade in at this deeper (for me) level.

Well if you want to test it the redneck way.
Find a very very small portable fan that you plug into a electrical outlet . open the drive bay cover door and either blow air into the unit or if possible suck it out the back.
It will need to be a small fan that you can place directly against the unit. or try your best with what you have on hand.
If you get the drive temps down below 60c I bet it will run.

_________________
VGA/PS2 Keyboard/PS2 Mouse/Serial debug board
Popcorn C-200
Popcorn A-200
Dune HD Connect
Rasberry PI OSMC(KODI)
ReadyNAS RN316
Amazon FireStick
Amazon ECHO
AnyDvD
MyMovies

But it *is* below 60 when it shuts down -- temps are at about their non-worst levels (the first number given for each drive) when shutdown happens. The "worst" temps are from an earlier period, before the fan add-in.