Hey everybody! Just wanted to come back with an update on my situation which I have finally resolved in the hopes that maybe my experience can be of benefit to somebody else. Because these problems seem so varied in their root causes, here's the specifics on my system and what I did prior to finally finding the magic bullet for my system (if you want to skip to the resolution, I've marked it out below):
Late 2012 21" iMac 3.1 GHz core i7
8 GB 1600 MHz DDR3 ram (factory installed)
1 TB fusion drive
Nvidia GeForce GT 650M 512 MB
No external monitors or other devices aside from some drives
It never had any problems of any kind all the way through Mojave. I updated it to Catalina 10.15.2 in December 2019 and kept it up to date without any problems into March 2020. Then with the 19E266 build of 10.15.3 which I installed on March 28, 2020 everything fell apart. I was getting 40-50 kernel panics per day and when it wasn't panicking, it was hanging leaving me to look at a beach ball for 5-10 minutes before then panicking. All the reports showed the watchdogD timer as the cause of the panic but, of course as we all know, that's just a countdown timer and something deeper in the system is the true cause.
I fought with it off and on for a few months because I've never met a Mac I couldn't fix before but it never got any better. Finally I gave up, wiped the system clean and did a full clean install of Mojave 10.14.6. Unfortunately, this did not solve the problems fully. It did reduce my kernel panics to about 3-5 per day but the computer was constantly hanging such that it was completely unusable. I could get maybe 10-15 minutes out of it occasionally if I was really careful not to make it angry. Apple suggested the problem was non-standard RAM but the RAM was factory installed. Then it was external devices but I had long prior disconnected all of them. Then the logic board supposedly was the cause at which point I called BS. I also had Linux and Windows 10 installed on this machine and when I would boot into either one, the computer ran perfectly. I ran a full slate of hardware tests and all the hardware checked out okay. I was ready to give up on MacOS.
Here's the resolution part:
Then one day I decided to beat my head against the brick wall again and booted it into MacOS 10.14.6 and started doing some troubleshooting. It immediately began hanging again but as I was working with it, I noticed an odd pattern--all my hangs had the timing and feel of a page file issue--like the computer was dumping stuff from RAM to a page file every time it accessed the disk. I checked the system monitor and my RAM usage was very low but I did see read/write disk spikes every time there was a hang. I started to suspect there might be a disk issue that my hardware tests just weren't finding. So, I took a new 1TB Samsung QVO SSD I had just bought, put it in my drive dock, ran a clean install of Mojave 10.14.6 onto it, changed my boot drive to the docked SSD, booted it up, and... TA-DA! (as my 4 year old would yell), it was perfect! It booted instantly, ran perfectly, and was faster than it has ever been in its entire existence! It has been over a month now since I did that and in that time I have had 0 panics, 0 hangs, rebooted twice just to avoid thunderstorms. Sleep/wake is fine. All external devices are fine. I've added an external display which is fine. Everything just works--the way a Mac is supposed to be!
I know this is merely one anecdotal report of my particular case, but my suspicion is that apple changed some low-level code or EFI stuff that effectively made MacOS unusable with fusion drives. I know they said Catalina was optimized for SSD storage but I didn't realize that meant nonSSD storage was now dead as far as system drives go. Maybe I'm off base and I just got lucky but if your situation sounds at all similar to mine, I'd try doing a clean install on an external SSD and see if it helps you too.
Good luck to everybody--I know this has been an absolutely maddening issue for all of us.