This should be easy to do, but I can't figure it out despite the fact that
there's lots of information in the forum and documentation.

Here's an example:

I want to mirror the website <http://www.oldwebsite.com> with everything
internally linked included. I want ALL external links to pages, images, etc.
to remain unchanged so that when a page is displayed with an image on a remote
site, the link still goes to the image on the remote site. If a link to a
remote site is broken, I want it to unchanged and still go to exactly the same
unchanged and broken link.

Once downloaded, I want to upload the mirror to <http://www.newsite.com/archive>
so that when someone types into their browser
<http://www.newwebsite.com/archive>, the home page of oldwebsit.com will be
displayed and the user can then navigate the site as if it were still located
at <http://www.oldwebsite.com>.

In other words, <http://www.newsite.com/archive> and <http://www.oldsite.com>
would look identical and navigate the same to website visitors.

HTTRACK is mirroring the site beautifully, but it I can't get it to leave
external links unchanged. It keeps sucking in remote images, etc. and storing
them.

I'm sure this has got to be very simple, but I am eating up a lot of bandwidth
mirroring the old website which is rather large.

This seems like it should be just about the easiest thing you could do with
httrack, but it has me stumped.