My preference is to be very specific and detailed.  People who want to help will appreciate this.   Most times, omitting details will result in respondents asking for them anyway.   Also, it is difficult to describe this concisely given the multiple aspects of the environment this problem arises in.   I do respect your opinion, however, and thank you for your help.

a hang

Are you sure? Did you try using ssh or booting to a console screen to check if it's not just a failure of the graphical desktop?

Pro tip: your OP is too prolix. A more concise description of the problem might help.

In order to analyze this, I unhooked the machine from the KVMS and placed it on a table that I use as a sort of "bread board" layout.  I have additional power supplies, keyboard, mouse, etc. there; there is no KVMS there, however.  Also, the video connection is VGA there because I use an older terminal for hardware testing.  I found that booting the machine, which had not been turned on for at least a year or so, was a bit random -- sometimes it would boot, other times not.  I went about eliminating possible issues.  I did replace a SATA cable and moved the hard drive to a different location inside the box.   These steps seem to have helped somewhat, and the PC began to boot reliably each time, not getting stuck at the "msi quirk detected" error.   I believed I had resolved the issue.  I could boot the box from the internal hard drive or from a thumb drive consistently.

I moved the box back to the normal place and hooked it back up to the KVMS.   The error message appeared again upon boot.  This got me to thinking about a posting I read while browsing for the mentioned error message.  It said that it could have something to do with the USB subsystem.   One solution is to disable legacy USB, so I tried that.  The problem immediately became clearer to me:  The KVMS is USB (and HDMI), and likely one of the older USB standards.  So I had to re-enable the legacy USB which allowed me to at least have keyboard functionality.

I think the problem may be with the mainboard, which is a 760GM-P23 (ironically, this board is manufactured by MSI, which has nothing to do with the "msi quirk detected" problem reported by the boot; the naming is just coincidental, though maybe the manufacturer is using the technological term for marketing).  The board is also denoted as "MSI 7641."   The board clearly continues to work, as I am able to fully boot it  with VGA.  The board has VGA and DVI but not HDMI.   I use a DVI/HDMI converter when the box is connected to the KVMS.  Nominally, the configuration works, but somehow this board does not seem to enjoy talking to the keyboard through my switch sometime after the initial screen blanking.

There are lots of posts about this online, but most of them are more than 10 years old; I would think this issue had long since been addressed in recent kernels.  This is (was) a popular board so its chipset should have made it into the kernel blacklist by now.   The solutions suggested (if any) don't seem to help with my specific board.  There are some more recent posts, but I found them to be in the context of other issues.  I note that kernel mailing list discussions about msi date back as early as the mid-2000s, so the devs were tackling that already.

Since my other PCs work reliably enough through the same KVMS, I am leaning toward the board or the kernel or both not being capable of handling the switch traffic after some point in the boot process.  This is only my guess though -- I am really not much of a hardware guru, and I have not studied Linux internals deeply (though I have plenty of Unix internals study behind me).

One other thing to note is that I vaguely recall that many years ago when this board was in a different case and I was using it as my primary machine, I had run into a similar problem when trying to install an early version of (I think it was) Mageia.  I forget what the resolution was now, but I think it had been corrected with a subsequent release.  I haven't used this box in some time, but it appears to run fine, overall, and the problem may be innate to that particular model/chipset.

I have some other boards here I could use, but they are new and I'd prefer to save those for my other machines as their hardware needs replacement.   I run some older generation, Athlon II and FX8350 amd3 platform kit.  Since the market for those is kind of long past, it is becoming increasingly harder to find replacement parts... at reasonable prices.  I have been slowly stockpiling older parts as I find them.  I know that I will eventually have to upgrade to more recent generation hardware, but I like using what I already have for the time being.

I might just be running into the problems of using older hardware, but I'm not sure.   I am hoping someone knows of a kernel patch or some additional options I can try.  So far, I have tried passing pci=nomsi, acpi=off, noapic, and combinations thereof with the msi quirk message and hang still occurring.