J. C.,
First - The output from your requested command of,
dir /a /q %systemroot%\registration >0 & start notepad 0
can be found in the file,
OUTPUT FROM dir _a _q %systemroot%_registration _0 & start notepad 0.txt
But, to save you time, there is no directory named Windows\registration
Back to your first suggestion - Back in Sept. I'd let Catalyst Control Center's autoupdate run to update the ATI graphics drivers to the new released version. Despite its claim that everything had updated correctly, and on the chance that something may not have updated properly, and the suggestion mentioned in your first link to uninstall Catalyst Control Center; I planned a clean install of the graphics drivers.
Immediately after starting the uninstall of Catalyst Control Center, I got the typical BSOD listing atikmdag.sys as culprit. I could no longer boot into normal Windows so, ended up uninstalling the graphics drivers from within Device Manager while in SAFEMODE. Following that, I was able to uninstall Catalyst Control Center.
Re-installing the drivers only, was another nightmare. Their installation program offered no option to install drivers without installing Catalyst Control Center. (I'd swear that was an option in the past) Anyhow, I was able to locate the folders where the drivers had been unpacked, so installed them by pointing to them from within Device Manager. Now, I am certain I've got the latest graphics drivers, and without Catalyst Control Center.
Hoping that might have solved the problem, I rebooted and still received the same BSOD.
I was about to give you the good news when I noticed the suggestions from Vir.
Vir,
I removed all extraneous ASUS motherboard stuff I could find. (I also uninstalled a bunch of other programs I'd not used in a long time)
There was a new BIOS released a couple of months ago. The only description about the update said it fixed an issue with large drive sizes when used in a RAID setups. Since I don't have a RAID setup, I'd decided at the time not to perform the update.
Today however, on the chance that the update included additional minor fixes that'd been left out of the documentation, (and that I'll try about anything at this point) I decided to update to the latest version. I now have the latest BIOS ver 1703.
Unfortunately, I still get the same BSODs.

(Did I mention earlier that even though each BSOD claims to have saved a dump, actually only about 1 out of 10 ever save anything in the \Minidump folder)
Interesting about the divide by 0 errors.
I ran a new BSOD file collection and attached to this post.
Unless either of you notice something new, I'm prepared to order a replacement graphics card. This time I may switch from ATI to Nvidia, though I've experienced issues with both in the past.
A semi-related question -
I mentioned that I'd uninstalled a number of under-used programs. Now I notice that autoruns.exe lists a number of registry entries refering to files that no longer exist. I've read that I should manually delete those entries. I've also read that I should leave them alone, Windows will cull them out of its own accord. Is either correct?
Many thanks to you both for your help!