Well, it worked with a "raw" Magento system taking it up to 1.5.0.1 Magento.  (UPDATE:  Worked on our Full DATA Version Also..)

1. Install Magento VM.
2. Run TKLBAM to get it in  the system (backup for the sake of it)
3. (I would like to try running TKL-BAM restore from Production Machine to get a Test Machine, but I am waiting for a terminally long Backup on the image I want).
4. Open SSH: https://yourserver:12320
5. install Subversion in SSH " apt-get install subversion" from Root Line
6. cd /var/www
7. (then issue the following command in its entirety (forget the link that I am seeing)

   svn export --force http://svn.magentocommerce.com/source/branches/1.5 magento

8. Open Webmin https://yourserver:12321, then go to File Manager
9. find /var/www/magento/var/sessions(delete all sessions)
10. find /var/www/magento/var/cache (delete all cache) - but leave the folder intact
11. cd /var/www
12. chown -R www-data:www-data /var/www/magento  (so that Magento Connect lets you in)
13. Upload to your Magento Root folder the file:  magento-cleanup.php which can be found on magentoconnect

14. open http://yourserver/magento-connect.php

15. back to filemanager (delete or rename magento-connect.php)

16. open http://yourserver   (you need to wait a little bit for the Database to be updated)

So this worked for me on a "newly born" TKL Magento 11.1    (now time to try with our data sets, but the Backup is Still Running over there).

I am optimistic.  This is the Footer (finally) which tells us the Version it is actuall Running!  Magento Connect Manager is also up to date (1.5.0.1)