SCarini wrote "As far as I can tell Border/Cont Search does not find the ellipse."
Actually, you're right on this. I did a quick test using a true ellipse (dynamic) and one with Approximate used and either 36 or higher arc segments. I wasn't expecting the true ellipse to work, but was surprised the segmented one didn't allow hatching on the outside of the ellipse and outer rectangular boundary. The contour search easily filled the inside but not so when on the outside!
What was possible using contour search was to fill the inside of the ellipse, then the whole rectangle (outside), then add a void by removing the ellipse-fill from the rectangle-fill.