I think you fundamentally misunderstand what a Funicular is. It is a gravity assist tool, much like a lever is a tool, a wedge is a tool, etc. It does not need to run from top to bottom, as in a transit system. You are simple using the weight of water (in this case) and gravity to assist you. It's an aid, which can pull other objects.
It's nothing more than a tool.
It doesn't need to be an either or situation. If the AE found it easier to pull stones up a grade, then they likely did that. If they found that and object being pulled by gravity, could assist them, then they likely used it as well.
Having an inner core, doesn't guarantee you stability. They could have built level by level, placing stones with a higher density towards the center.