Right, I've had nearly 24 hours to chew this one over and this is what I think now!
Miss madam IS making a fuss about being left too long on her front or her back because she is not used to it. This is because she hasn't learned to deal with being on her front or back for very long. This is because when she moans at being on her back (or front) for too long, mr or mrs molgrips picks princess up and gives her a cuddle.
So one answer is to leave her a little longer (each time) on her front (or back) with toys to stimulate her. Give it a few days and she will be happier on her front (or back) for a longer period.
It's tough love time I'm afraid.
OR you could design / commission a larger than average doorway bouncer / activity centre / play nest and see how you go with that.
But this really is about attention and manipulation and not about special seating arrangements – sorry!
What do I win?
As a father of two boys 12 & 10, what he ^says is right