So, I've fiddled about a bit more and I seem to have gotten it working (sort
of). I am now booted in and writing this on Trisquel 8, using LXDE. Woo hoo!
:-D
To fix it, I booted into single-user mode. When I ran `sudo apt-get check`,
there was a list of broken package dependencies. Not that many, and most of
them seemed to be related to Texinfo. When I tried to run `apt-get -f
install`, it didn't work (presumably some of those packages couldn't be
fixed). So, I removed some of them with `dpkg -r`, to the point where
`apt-get -f install` did work. At that point, apt kicked off into setting up
a big list of packages, which took quite a while. So, it seems that perhaps
the broken packages may have interrupted apt's upgrade process, which is
probably why it broke my system. After it completed all that, I ran `apt-get
upgrade` again and eventually apt got the system to a point where it was
happy enough to boot into LXDE.
Another package that was causing problems was plymouth-theme-trisquel-logo,
which I had to remove completely. After the upgrade, systemd was installed,
but upstart hadn't been removed, so I removed that too.
So, I seem to have gotten there in the end, although I wouldn't say the
experience was completely 'smooth'. There are probably some things that
aren't working quite right. If I see anything then I'll try to figure out
what packages they are see if I can do anything to fix them.