I sought out help directly from Github for Windows. I received a very prompt response with a solution that works.
There are 2 steps:
1) Set the Github for Windows options for default shell to Custom and put the path and executable for the Console.exe. I was already doing this and there are screenshots in the question above. (Make sure you hit that update button to save your changes)
2) In the Console2 'Shell' text box in the 'Tabs' section you'll need to put this:
bash.exe --login -i
No path required, just the executable named bash.exe (this is magic to me). The Console Settings should look like this:
A couple of gotchas... I was advised to leave the Startup Directory blank in the Console 2 settings (I think this is so that the startup directory in Gitub for Windows GUI is honored) and that the Github for Windows tab should be the first in the listing of tabs. Another gotcha I discovered is that you can no longer use the Console.exe directly to start up your shell. You must use the Github for Windows shell shortcut that gets installed.
Otherwise you will get an error that says, "Unable to start bash.exe --login -i!"