You wrote, 'A royal cubit is geometrically defined as 1 x π/6, i.e. 1/6 of a circle whose diameter is 1 meter.'
This produces a royal cubit length 523.6mms/20.614".
The mean length of the royal cubit in the GP's King's Chamber is 524mms/20.632".
However, the standard cubit (6 palms or 24 digits) is clearly anthropometric in origin and the royal cubit is simply a standard cubit with a palm added to it and therefore also is anthropometric in origin - and not 'geometrically defined'.