You're welcome to try to hack it in there. The reason it's not a simple pasting of code is because we have different parameters for redirecting the user, javascript that must also be called, and some library functions from the JFBConnect component that we use as well. Connecting and interacting with Facebook is pretty complex. We'll see if we can make a more hybrid module or some other easier method for you to use.
As for the duplicate logout button, can you 'hide' that in the cblogin module to enable you to use both?