@JonL … I think I ran into this when I upgraded from patch 5 to patch 6. My setup is like yours - Win2012 with remote SQL Server 2012 also on Win2012. The upgrade failed at the very end and seemed to want to use the SQL Server userid of “sa” when we defined our own id for this. I ran the installer two more times - the first time I was prompted to uninstall, and the second time it went through the full reinstall, asking me for connection details, etc. The process didn’t seem to delete anything database related. After this, the upgraded succeeded and my server was back. See below:
Perhaps it will be of some help.
–Mark