I understand that I can log to the console when using a Firefox extension with the cfx run command.
Is there a way to log to a console after the extens
Have you tried console.log() with Firebug? (I know you have tried Application.console.log() and Firebug.console.log() already)
I just tried it in the Web Console on FF16 running Firebug 1.10.4 and it seems to work: 
Here are some more examples from the Firebug Wiki itself: FirebugWiki Console API
Additionally, you can write messages of different types in the console, such as: console.debug(), console.info(), console.warn(), console.error()