Having just waded through the "Manual Install after a failed automatic install" blurb, I was trying to use regedit and believe the paths for 64-bit were correct. Sadly, they weren't!
SOFTWARE\\Red Gate\\SQL Backup\\BackupSettings\\(LOCAL)
SOFTWARE\\Red Gate\\SQL Backup\\BackupSettingsGlobal\\(LOCAL)
are where I found the nodes, NOT under the HKEY_LOCAL_MACHINE\\SOFTWARE\\Wow6432Node\\Red Gate element, which contains no reference at all to the above Backup% key names.
Please check the installer vs. the documentation.
Windows Server 2008 SP2 - 64-bit.