Aaaahh, the glued ones ("good shadow") CAN be duplicated "in one piece" by ctrl-dragging!
So, seems that they do almost everything I need....
Except that it does not seem to be possible to fully use the format brush between them because the shadow is lost, then.
So if there is an easy way to make my "glued group" shape into a proper "one piece" shape, I'd be happy to know about it.
BTW, the document is attached in the first post.