Adobe Flash hard freezes computer in all browsers!

Yeah, registry cleaners can definitely leave the machine in a bad state.  Microsoft has a lot to say about them, all of which basically comes down to "don't".

I'm definitely not aware of a widespread issue where we're taking down machines.

We don't have direct access to the hardware, so it's pretty difficult to take the whole machine down ourselves.  What's much more likely, is that we're calling into an intermediary Windows API in a totally reasonable way, but in the context of your system, it tickles the thing that ultimately brings the system down. 

In most cases, this is usually a case of ticking a video driver bug.  The driver *does* have direct hardware access, and can definitely bring the whole machine down.  This is why I was asking about disabling hardware acceleration.

In your case, it sounds like Windows might not be in a great state.  Instead of a driver issue, it might be a privileged system call (windows kernel, etc.), which ultimately leads to the crash.  A scenario where a privileged system call gets some garbage (or nonexistent) registry data and then operates on it would be a pretty reasonable guess. 

Analyzing the crash dump and tracking it back to some discrete action that you could take to "fix" the issue would be far more painful and time consuming than doing a clean install, and would likely have a much, much lower chance of success.  It sounds like you've already explored the reasonable things.