Solution
- I extracted ALL of the files in c:\windows\installer from the backup of another CU9 exchange server.
- Then moved them into a folder on EXCH01 (the one with the issues).
- With File Explorer in Details view, I added the "subject" column.
- Going through the registry:
Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Installer\UserData\<user>\Products
- In each entry, look at the "InstallProperties" key
- Compare the "DisplayName" to the Subject column
- Rename the msi according to the "LocalPackage" value
- Move the renamed file into c:\windows\installer on the afflicted computer
Once all the MSIs were put back in place, the installer ran through. There was only one other issue where I had to manually make a "grammars" folder.