Dan,
Not sure what issue you were having with not being able to logout. Our 4.1.2 release (out yesterday) does have a fix for a logout bug similar to what you mention. However, you need to use a JFBConnect logout button for auto-login and logout functionality to work perfectly. If you're using the logout button from another extension, that may be the problem. We're working on a better solution, but for now, that's the only suggestion.
As for login window, you're correct. After the session timer expires, the user will be automatically logged out. That's how Joomla works, and we can't get around that. The only things we can recommend are: a) Enable auto-login or b) increase the session timeout.
Hope that helps, but if you have any other questions, just let us know. Glad you're happy with JFBConnect, and yes, it's smoother than JomSocial simply because it's what we do day-in and day-out
Thanks,
Alex