My gut feeling on this is that they took things further that Pi when they went to 9.87654321 and knew this was a good representation of Pi squared. So the thinking behind the system goes beyond Pi which is left behind.
The reason is Rhind 50 x the Nippur cubit is 5.333r so they worked two units off against each other to produce the eclipse system as 32/6.
It has to be remembered that this was secret knowledge so actually looking for proof it was being used is a huge challenge. The obsession with all things solar defines the society possibly.
Based on these calculations I would suggest the Pi investigation is at Stonehenge and the results of the Pi investigation have been fed into the GP design using the Canon of Ancient Measure.