So, seem to have made progress. With domain mapping etc, when I click dashboard on the sites panel for site1.example.com it brings me to:
https://www.site1.com/wp-login.php?redirect_to=http%3A%2F%2Fsite1.com%2Fwp-admin%2F&reauth=1
And if I login, it brings me to the WordPress installation at site1.com, not site1.example.com.
Make sense?