Controlling face overlays from different photos

Hugin does provide a fairly simple mechanism for controlling situations such as the one you describe (where different pieces of images of faces are inappropriately combined from different images). This method requires that the images be in a format that provides an alpha channel to control transparency. In my case, I

1) Converted the original images from JPEG into PNG. (JPEG seems not to support alpha channels).
2) Used GIMP to activate an alpha channel layer for the image.
3) Used GIMP to "paint" the alpha channel layer "off" (fully transparent) for the parts of the input images that I wished to exclude from the final merged image.
4) Export the modified image as a PNG file (large, but temporary), then built the final panorama from these modified images.

In this way, I was able to select which of the redundant image elements would be excluded and eliminate the "chopped image" appearance that you describe. Note that this feature is strictly "on" or "off". Gradations in the alpha channel are ignored.