After some more checking on the contents of the /Recovered Items folder left over after my failed upgrade of OS X from Lion to Mountain Lion I decided to proceed with re-installation of the components to see if I could get things back as they were again.
The first step was to install the Server component again (which has gone missing after the upgrade). This only took a simple purchase of the Server.app component in the App Store. After that I had a Mac Server again and could start my reinstallation.
The first component to reconfigure was the Open Directory component. It was extremely important for me not to lose that one as it contained all my users, their passwords and group membership as well as all the e-mail addresses each user had (I am hosting a few different domains, re-creating that would mean a lot of work).
When I enabled the Open directory server component, I had to specify how I wanted to configure that. This screen included an option to import a backup. As I still had the whole data structure from my previous installation, I tried that first but that did’t work. Then I noticed that the directory /Recovered Items/private/var/backups/ contained a file called ServerBackup_OpenDirectoryMaster.sparseimage that was less than a day old. I selected that file as backup, which was accepted to restore from and it looks like that did the trick. My users were restored and I could also login with my regular userID again.
Based on this initial success I decided to rebuild the rest of my server as I knew the other components (PostgreSQL, Postfix, Dovecot, etc) pretty well from when I hosted everything still on Linux… I will continue to document the steps I took as well as my custom setup as it may be useful for others.