The process typically includes a "fill basins" step. This step fills basins. If you have a ring of land, it's making a basin. I'm not sure that there's much you can do with that process, unfortunately. Selecting an area to be processed does the full normal fill basins and then blends the old and new surface according to the selection, which will leave a steep cliff in the area. I should probably modify the processing on fill basins to allow for a true selection that will treat unselected areas as sinks and so allow for interior basins with a careful selection.

A nasty workaround is to duplicate your height map and cut a channel on one side of the ring in one of the maps and on the other side in the other map. Then process the two maps and blend them with an image editing tool. An ugly solution, but possibly workable.