Wow, that'll teach me to assume I'm dealing with a thread that I've been working with during the day without checking.
Sigh. Sorry.
The best thing to do here is to do what you suggested originally - copy directly to the new drive (in a temporary case/dock), then swap the drives. A drive dock is <$50 and quite useful, but if you have to back up to a separate drive then copy back, that's OK, it's just slower.
There's no need to install an OS to the external, since you'll be copying it to the internal. Just partition it properly before you start.
Now THAT response should make sense.
(Sorry, again.)