An instance of SQL Server 2012 Express became corrupted somehow.
I suspect it was related in some way to my use of Entity Framework, but have no proof yet.
When
This advice from TechNet worked for me:
Following Registry-Key must be set to 1[...]:
HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Windows\AppCompat\sbEnable = 1
In my case that registry directory did not exist at all. And the uninstall was STILL stuck at that location for several (less than 10) minutes. But eventually it continued and finished.