After stalling out this last attempt (and then I closed the program), I got a
warning/pop-up.  First time that's happened in the 6-10 times I've tried it,
and stalled/crashed/closed it.

The popup window said:
Error deleting a hts-cache/new.* file, please do it manually

I went looking in hts-cache/.  Found nothing that seemed like it should be
moved/changed/deleted.  The readme in hts-cache didn't tell me a blessed thing
either.

But the work-around for me was to download the directory html off of the
original site, delete out everything until where HTTrack should've been
starting, add a base href to that resulting html, and then put that up on a
website, and point HTTrack at that, and tell it to browse anything on the web
(whoops, forgot that the first time and had left it domain specific, which
only got the html).

A gig or two down, 14hrs in - and it looks like this might go the distance. 
I'm gonna let it run.  I'm going to make the assumption that the files are
actually valid, and if it works, then I have no more questions. :)

If you care to make it more user-friendly, I've already gone thru the things
that are as clear as mud / not user-friendly.