UPDATE: ISSUE RESOLVED
I can't believe I didn't think to look at the actual Windows Event logs myself. Chris, your suggestion to look at that is what I needed to solve the issue. So if you look at the log messages I posted in my last message here, you will note that it was the .NET Framework that was reporting an application fault in _Setup.exe. That got me thinking. Most of the systems where I have the problem were fairly new clean installs of Windows 10 1511. As a result, I had the default .NET Framework 4 installed but not the .NET Framework 3.5 which has to be specifically added because it is not installed by default.
I added .NET Framework 3.5 and that resolved the issue.
Request: I'll post this to my case as well, but I would like to make the suggestion that the setup maybe check to see if .NET Framework 3.5 is installed or not and either offer to install it or at least prompt the user to install it. In my experience, applications that need it usually tell you when you try to install them that you need to install .NET Framework 3.5. That would be a far more desirable mode of behavior rather than the _Setup.exe simply crashing.
Thanks to all who have responded here in helping me to figure this out.
- Hannes