I was wondering why can't I bloody well select and copy the text in front of my eyes. Especially when others say you can just "select and copy". Turns out you can, you just have to start the drag outside of any text (i.e. in the gutter above or to the left of the text) as any mousedown -- whether it's a click or drag -- on any text immediately invokes the property editor. You can also click outside text to get a cursor (even if it's not always visible) which you can then move around with the arrow keys and select text that way.
The text copied to the clipboard is devoid of any indenting, unfortunately, but at least it saves you from manually transcribing the entire contents of the CSS file. Just have your diff programme ignore changes in whitespace when comparing against the original.