That's an interesting idea you mention. In that case it seems you see the lower portion as simply a ram pump pool contained by the surrounding moat. Creating a water source or artificial lake with no other particular purpose other than a water source. Is that what your implying?
The problems I have with that is that the final construction complete with casing stones then becomes an adaptation of convenience coincidentally benefiting from that early construction as if it was a design based on harnessing that early construction for its purposes. But that means its almost too convenient that the early construction seems almost a perfect system to serve that reset of the pyramids purpose.
I see the entire system being perfect in its entirety with nothing appearing to be harnessing an earlier purpose as an adaptation. In other words, for me to follow that time line of construction, it would imply that the grand vision of that entire project was completed at the very beginning before breaking ground but that vision and focus was miraculously maintained spanning thousands of years.
Its like that guy with the "TO DO" list from his wife had successfully put it off longer than any other man in history, and his wife gets the award for longest focused nagging victory of all time. Or that game was played over millennium maintaining the positions of nag and ignore like a religious devotion over generations.