Here's a partial solution. After you make your changes, click on one of the links to the relevant file. This is the original file, so you'll have to refresh the file, which is under the options menu button in the upper right of the firebug pane. Now you have the modified css page, which you can copy & paste. Obviously, you'll have to do it for each css file.
Edit: looks like Mark Biek has a quicker version
