Jon,
I very much agree that hands on compass and straightedge exploration can be extremely enlightening. Call it a "graphical" approach, a "naive geometry" approach (a term I believe first used by Jens Hoyrup), or an "empirical geometry" approach (my term for this), it is simply a means by which one can derive all kinds of interesting and useful correlations and connections. Euclid is chock full of this stuff - though in Euclid everything is "proven". It is most likely that in the Egyptian context proof was perceived in a much more empirical way.
For instance, all evidence points to the fact that they were aware of the properties of the 3-4-5 right triangle. However, this does not mean that they had any knowledge of what is now termed the Pythagorean Theorem. They just simply knew from direct measurement that a right triangle whose sides were 3 and 4 units long respectively would always have a hypotenuse that was 5 units long - and further, that this relationship held for any multiple - such as for 24-32-40, etc. I should think that they had no inkling that a more rigorous and general proof even existed.
The same goes for their graphical constructions. In their area of the circle algorithm, for example, they correlated the circle's area with the area of a square whose sidelength is 8/9ths the length of the circle's diameter. We, of course, know that this isn't an exact correlation, but did they? And even if they did, did it matter? More than likely they felt that it was absolutely correct within the context in which it was being used - exact or not. It was Ma'at. Plus, it was simple to remember and convenient to employ. What's not to like?
You ask, "Why I wonder does nobody ever seem to draw circles etc all over the East-West cross section of the Great Pyramid?" This is a great question. It would seem that east/west was equally as important to them as north/south.
Best,
Lee