I solved the crashes!
It had nothing to do with the Unofficial Service Pack, the high-speed CPU fix, or the eXtended USB Supplement. Instead, the culprit seems to have been a wonky Explorer Shell-extension for one of the apps I like to use.
Here's how I found out:
Since the error-message itself was not very helpful, I ran Dr. Watson to see if he could tell me more. Watson gave very full reports on each crash, but unfortunately the only clue I was left with was the information that an unknown module was trying to write to memory that doesn't exist. Quite cryptic, but following that trail led me to this thread over at Microsoft's TechNet, in which the OP describes a problem similar to mine (but on Windows 7).
A helpful answer from Luigi Bruno in that thread indicated a way to finding out what the faulting module might be:
The reported exception code ... indicates that a memory access violation occurred: a module loaded in the Explorer.exe memory space tried to access a memory location it was not allowed to.
The detail recorded in the Event Viewer does not indicate the faulting module, so you have to perform a step by step analysis: download and run Nirsoft ShellExView, which will provide you with the complete list of the shell extensions installed on your computer and allow you to easily disable and enable each of them; start turning off all the non-Microsoft extensions and watch your system's behaviour. Then re-enable each of them on a one-by-one basis until you'll find the faulting one.
At first I thought I'd have to hunt down an older version of the app or one similar to this one, but surprisingly Nirsoft's ShellExView and ShellMenuView both run on Windows 95!
The attachment ShellExView_on_Win95.png is no longer available
Firing up the app I immediately spotted five extensions with a slight reddish highlight on them (the app does this for non-MS extensions).
I confirmed these were the suspect ones, by using the option to hide all non-MS extensions.
There were three extensions for PowerArchiver (a WinZip clone), one for Wang Image and one for DiskTools. Since ShellExView cannot disable extensions on Windows 95 or 98, I used the Open CLSID in RegEdit-context menu option to point me to the offenders in the registry, then used the Export-feature in RegEdit to make a backup of each entry (in case deleting them would cause mayhem), and then deleted those branches. I'm pretty sure I've confirmed the offender is PowerArchiver, since I haven't installed that on the newer system (used 7Zip on that one, for some reason) and because the other suspicious extensions were also present there without the crashes manifesting.
After deleting the registry entries for the offending extensions and rebooting, I have not had a single crash!
XUSBSUPP exonerated!
FIX95CPU exonerated!
Unofficial Service Pack 1.05 exonerated!
Cacheman exonerated!
Bill Gates exonerated! 😁