I am just curious and would like to know what evidence do you have that leads you to think the Ancient Egyptians passibly used methods similar to ours in determining a value close to the current meter? I am not saying you're wrong, but like Thor Heyerdahl once said: Progress is man's ability to complicate simplicity.
From my perspective one must keep in mind the simplicity of the Egyptian system of mathematics and how it compares to the complexity of our current system. Nor should one should not assume the AE value of 39 3/8 inches we perceive as their meter was a result of the same factors and methods we used to determine the meter length? From my perspective it is not possible to comprehend what they did using our methods and values.
Please do keep in mind, as per my drawing, their value 39 3/8 inches has the same 21/11 ratio to the 20 5/8 inch cubit as the 345 triangle and a the maximum size enclosed circle for both area and/or perimeter/circumference.