The installation went without a hitch, and LibreOffice started just fine. But the UI was ghastly, horribly, I would-rather-look-at-and-smell-a-garbage-bin ugly.
# apt-get -t squeeze-backports install libreoffice-gtk
There is a libreoffice-gnome package as well. I don't know what the difference is yet, but I suspect it would be a good idea to go through all the libreoffice backports for Squeeze to see if there's anything else I missed.