After more trawling, found a tip from a couple of months ago on the Admin forum.
[URL]http://www.kde-forum.org/post/57994/lastpost.html#post57994[/url]
At first, I thought changing the environment variable KDE_MULTIHEAD
from true to false would do the trick, but it doesn't - kcminit overrides it
at start time.
It seems you need to edit your kcmdisplayrc file
(mine is at ~/.kde/share/config/kcmdisplayrc, yours may vary)
to find or create the [X11] section so that it reads
[X11]
disableMultihead=true
Now, display :0.1 is completely blank, with no kde stuff on it at all,
but you can still use it to run your app.