Just in case this happens to anyone else: when I load the Cookie Clicker page, there is a notification telling me to occasionally save an export from the "options" link. Looking on this help forum, it also says I can export via the "menu". However, when having the "Shut Up" plugin loaded (blocks comments) there doesn't seem to be any "menu" or "options" link. Turning "Shut Up" off reveals the menu in the center section of the screen, above the visualization of the buildings.
Not sure why this plugin designed to block comments also blocks the menu here (I assume it's an overlap with the naming of a div or something), but there it is.