-- MANY THANKS, JDC! --
That wasn't it, but you pointed me in the right direction.
When the procedure still didn't work it got me digging further into the documentation about session management, and I found this nugget down at the bottom of the Cms Roles Provider Documentation (found here: http://www.bettercms.com/documentation/roles-management#cms-roles-provider )
"Please note, if you have line <remove name="FormsAuthentication" /> in your configuration, remove it otherwise it will disable BetterCms side panel and edit content functionality."
Which I did have in my web.config. Once I commented that out it works perfectly.
So thank you JDC, for getting my head in the right space, and Eduard, check for that node in your web.config.