Windows – Fixing Volume Shadow Copy (VSS) System Writer / CAPI2 Event Error 512 on Windows 8

For many years now, Microsoft's Volume Shadow Store (VSS), also known as Previous Versions feature, has been built into Windows. It is still there in Windows 8, and the former Windows-7 backup feature uses it, as do other features.

In my event log I am getting this error:

Event #513, CAPI2:

Cryptographic Services failed while processing the OnIdentity() call in the System Writer Object.
Details:
TraverseDir : Unable to push subdirectory.
System Error:
Unspecified error

From google, and microsoft forum searches, it seems this can be caused by the "System Writer" being missing from the VSS writers list, which you can view by going to an elevated Admin command prompt and typing:

vssadmin list writers

I did this, and it does seem that there is no writer named "System Writer" in this list.
However, none of the fixes (usually involving using icacls command line tool to modify NTFS permissions) are working for me. In particular, I cannot modify any permissions of any files in the C:\Windows\System32 folder because the folders I am trying to modify are owned by some special user named TrustedInstaller, and thus icacls running from the Administrator context cannot write to it. One folder that apparently needs write access by Admin user accounts is C:\Windows\System32\WinSxS, and it is marked read only for every account that even has read access, so by NTFS permissions it has been marked as unwriteable. This may be as designed (correct) in Windows 8.

So I am stuck and not sure how to proceed. I believe the CAPI2 Error 512 is being generated every time I try to do a backup using the Windows 7 File Backup feature in Windows 8, which is what they renamed the real Win7 backup mode to in Windows 8, since they replaced the real backup from Win7 with a pseudo-backup program in Win8.

In a nutshell, the question is: How do I fix this Volume Shadow Copy fault CAPI2 Event 512, so that this event log error and the underlying VSS-System-Writer-missing problem goes away.

I suspect that this problem may reproduce on other Windows 8 user's systems IF they use the "Windows 7 File Recovery" feature. The new "File History" feature seems to have been intended by Microsoft to supercede this feature, however the File History feature does not function in a way that I find useful, so while trying to get the Windows 7 File Recovery (the new name for Windows 7's regular Windows Backup utility) working, I have hit this roadblock which appears to be blocking Windows 7 File Recovery from working.