Of course, there is no "correct" way to combine a stack of times of star images with a single image of something that does not share their apparent motion. Was of overcoming this lie in the art field of "astroscapes," not in scientific imaging...which is where PI operates most readily. You might just look up some well known artists in that field...Alan Dyer comes to mind. I think he even may have written a book on the topic.
Alexw