For what it's worth, after upgrading to KDE 4.6.3, I tried the suggestion of unsetting QT_PLUGIN_PATH again with the pre-compiled 0.3.4 Sigil version, i.e.
Code:
$ QT_PLUGIN_PATH= /opt/sigil/sigil
and it does work, at least at first glance. I haven't wrung it out completely yet.
Previously I was using KDE 4.4.something, but I may also simply have made a typo when typing in the command.