iMac 2017, 10.14.6, Frequent Hangs and Restarts, EtreCheck Report Attached.....

See if you have a panic report (file's ending in .panic).  If you have more than 1, please post a couple as the differences can be very useful:

Look for the Kernel Panic reports at:

Finder -> Go -> Go to Folder -> /Library/Logs/DiagnosticReports 

<http://support.apple.com/en-us/HT200553>

The panic report should have ".panic" in the file name.

You can put the panic report in an "Additional Text" box when you Reply

If, AND ONLY IF, you have difficulty posting via "Additional Text"

then try posting to PasteBin.com, and give us a PasteBin URL link.

<http://pastebin.com/>

I'm going to suspect 3rd party RAM

Memory Module: BANK 0/DIMM0, 16 GB, DDR4, 2400 MHz, 0x859B, 0x435431364734534644383234412E433136464244
Memory Module: BANK 0/DIMM1, 4 GB, DDR4, 2400 MHz, 0x802C, 0x344154463531323634485A2D3247334232202020
Memory Module: BANK 1/DIMM0, 16 GB, DDR4, 2400 MHz, 0x859B, 0x435431364734534644383234412E433136464244
Memory Module: BANK 1/DIMM1, 4 GB, DDR4, 2400 MHz, 0x802C, 0x344154463531323634485A2D3247334232202020

Each and every one of your Panics are different. And in 2 of the cases they are memory related.

Bad tailq elm

is staying an address in a linked list is not properly formed.

Spinlock acquisition timed out

is an in-memory abstraction that allows multiple processes to make sure they sequence access to some critical data structure. If the memory location acting as the spinlock drops a bit, it may be the bit that says the lock is unlocked, so the waiting thread(s) would spend too long checking the spinlock memory location looking for that bit to get properly set.

Or the thread that has taken control of the spinlock, dropped a bit in the spinlocks address, and released the wrong memory location.

You can try running Rember, but if it DOES NOT find anything that does NOT mean your memory is not bad, as the bad memory could be in use by the operating system, and not being tested by Rember. But if it does find something, you can present that information to your 3rd party RAM vendor

https://www.kelleycomputing.net/rember/

Suggest booting int Safe mode to get the maximum amount of RAM to Rember for testing. Also set the repeat count to maximum and let it run overnight.

iWow, thanks for the interpretations and suggestions, Bob! I purchased the iMac with 16Gb Apple RAM (2x8) and added 32Gb RAM from OWC (2x16) for a total of 40 Gb. I’m going to pull the 2 16Gb "brand x" sticks and keep my fingers crossed. Will report back. Boy, I hope it’s the RAM—I’m beginning to think it’s the logic board.

Otherwise, the hanging on restart and frequent crashes and restarts continue, despite having done the following, and it seems to be worsening. When it finally boots up, it crashes after several minutes. And now I've seen the "Prohibited" symbol on startup a few times.

I have:

Reset SMC and PRAM

Disconnected all peripherals

Run Onyx and Cocktail maintenance 

Booted in Safe Mode multiple times, but only successfully once, and it crashed and repeatedly tried to restart after an hour.

Booted in Recovery Mode many times, only successfully once. 

Was able to run First Aid—no help. 

After many tries, was able to Restore OS in Recovery Mode, after erasing and reformatting 1TB SSD drive as APFS. That new install hangs and crashes, too.

Tried to boot from two different external Mojave BU clones, but failed to Boot—hangs and restarts.

Failed to complete clean install of 10.6.4 via fresh USB stick Installer I made on my MacBook—boot stalled 

Tried to do second clean reinstall from a fresh internet download while in Recovery Mode, but crashed when Mojave download was at 6.4 GB out of 8.

OWC is a reliable vendor, and will replace their RAM. Especially if you have evidence that it is failing.

Taking the RAM out is a VERY good way to test. So while it may be painful living on 16GB for awhile, it is a good test, if you let it run long enough.

Unistalled the two OWC 16 Gb sticks, and the machine booted up lickity-split! After 30 minutes, all is well. But I won't formally celebrate until I check in on it in the morning.

Thanks again for your help, Bob!

Bad RAM it is! Computer still up and running fine this morning. So relieved it's not the logic board.

Since the RAM sticks are so accessible on many iMac models, Perhaps we should add "RAM removal trials" to our erratic-start up -and-frequent-crashing algorithm.

By the way, I purchased the iMac with 2 x 4 Gb RAM sticks, not 2 x 8. So I'm limping along on 8 Gb. And, I have two apple ID's from the old old days, and inadvertently used both in this thread.

Very grateful to you, BobHarris!

Apologies for a not-so-stylish late entrance...

It sounds like you have this sorted but I spotted a couple of things that still concern me. They may be worth considering if the KPs return after you add the replacement RAM:

1) Try testing with the external drive(s) disconnected. I cannot tell if you have a pile of externals or one or two that are heavily partitioned, but some external drives' controllers can be wonky. Simple enough test.

2) Maintain and DiskWarrior: Cocktail and DW were indispensable tools in the infancy of Mac OSX. It was hard to run without them and other tools like TechTools and Onyx. Today, the macOS is hugely more sophisticated. Auto-maintenance routines are more refined and effective, andbuilt-in protection has improved immensely. The system simply takes very good care of itself. Now running Mojave, I no longer rely on any third-party utilities that 20 years ago I would not have ever been without.

There is the chance the the Maintain stuff and DW are now interfering with newer Mac OS protection and maintenance schemes. A couple of clues:

Kernel panics - This system has experienced kernel panics that could be related to 3rd party software.

and this, in Diagnostics:

2020-07-28 14:51:59 Cocktail.app Hang

Executable: /Applications/Utilities/Cocktail.app

See if you can disable both ad test if you have recurring KPs.

I don't think Logitech software is your issue. I've run it since the late Pliocene on all our Macs and never had a hiccup. The only caveat is to not trust their software update display. It tends to report an update available but the interface makes it look like it is offering the same SW version you currently have. Ignore that. If it says there is an update pending, there is—regardless of the version shown. If no update is pending, it is clearly stated.

Call OWC. They will provide you with replacement DIMMs.