It seems there is no way to "actually" do this. What I ended up doing was faking it, if someone has a better answer I'll be happy to accept that.
I used the value of ScaleFactor as such:
scaleFactor = ((double)Application.Current.Host.Content.ScaleFactor) / 100.0;
Then I created the writeable bitmap as such:
screen = new WriteableBitmap((int)(cl.ActualWidth * scaleFactor), (int)(cl.ActualHeight * scaleFactor));
And placed it in the background with:
backgroundImage.Stretch = Stretch.Fill;
It seems that this is actually using the image properly and mapping pixels of the image to the screen rather than scaling them. This is a bit hackish so if there is a better solution I'd be glad to hear it.