Downgrading Internet Explorer 9 into 8 on Windows 7

That should be an easy task, right? You guessed it. If I'm writing about it, it isn't. Once in a while I still test with a real IE8. The IE10 and IE11 emulators should be good enough, but they aren't. Here are the stats from this blog:

People seem to run with IE8 a lot. They shouldn't but ... they do.

Here is what I did:

1. List of Windows updates installed on the computer:
   
2. Managed to find Internet Explorer 9 in it (on Windows 7, that's pretty normal):
   
3. Un-install starts:
   
4. Yep. It took a while and hung. Darn!
   
5. I waited for 20 minutes and rebooted the hung piece of ...
6. Reboot did some mopping up and here is the result. No IE anywhere:
   
7. Guess who cannot re-install it. On a normal installation it is listed in Windows features, like this:
   
   In my case, no:
   
   

No amount of reboots, running sfc.exe or anything I can think of will fix this. This is what I already tried:

1. Attempt fix with Windows Resource Checker:
   PS C:\Windows\system32> sfc /scannow
   
   Beginning system scan.  This process will take some time.
   
   Beginning verification phase of system scan.
   Verification 100% complete.
   
   Windows Resource Protection did not find any integrity violations.
   It simply fails to restore the files, because all the bookkeeping says, that IE8 shouldn't be there!
   
2. Let' just download the installation package and re-install manually. Download Center - Internet Explorer 8
   
3. Ok, we're not going to do that, because the IE 8 installation package for Windows 7 does not exist. Reason is very simple. Win 7 came with IE8. It is an integral part of the OS. You simply cannot run the Windows 7 without some version of IE. No installation packages necessary, right? Internet Explorer 8 for Windows 7 is not available for download
   
4. Right then. I took the Windows Vista package and ran the installation anyway. All the compatiblity modes and such yield the same result. Internet Explorer 8 is not supported on this operating system
   
   
5. Re-installation instructions, part 1: Reinstalling IE8 on Windows 7. Not much of a help. The
   
6. Re-installation instructions, part 2: How to Reinstall Internet Explorer in Windows 7 and Vista. No help there either.
7. Registry tweaking into HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Winlogon\GPExtensions to see if {7B849a69-220F-451E-B3FE-2CB811AF94AE} and {CF7639F3-ABA2-41DB-97F2-81E2C5DBFC5D} are still there as suggested by How to Uninstall IE8. Nope. No help with that either. That article mentions "European Windows 7". What could the difference be?
8. Perhaps re-installing Service Pack 1 would help? But well... in Windows 7 SP1 cannot be re-installed like it was possible in Windows XP. That actually did fix a lot of operating systems gone bad at the XP-era.
   

The general consensus seems to be, that you simply cannot lose IE from Windows 7. Magically I did. Just based on the Wikipedia article about removing IE, it is possible.

Some of the symptoms I'm currently having is Windows Explorer Refuses to Open Folders In Same Window. Some of the necessary DLLs are not there and Windows Explorer behaves funnily.

I don't know what to attempt next.