Joe: "If it was so important to the builders of the GP for the South KC shaft to line up with just that one star in Orion's belt, why did they allow the angle to vary by more than 5 degrees?"
This initial variation of the slope 39.2 + 50.54 + 45 degs was probably carefully considered as the mean of these three angles is more or less 45 degs or sqd 7 - the angle of incline for the final 42.75 m to the top end in the core masonry.
In Badawy's proposal, the shaft is targeting the distinctive 3-star asterism in the centre of Orion.
The centre E/W axis of the sarcophagus chamber is offset 21 cubits from the E/W centre axis of the pyramid. If the floor lines of both the north and south shafts are extended down to where they intersect below the chamber's floor, the point of intersection is 22 cubits from the E/W centre axis of the pyramid.
The outlets of both shafts high above in the core masonry are close to being at the same level above the base of the pyramid, which means the shafts were probably designed with symmetry in mind - the basic 'framework' for the design based on sqd 7 for the south shaft and sqd 11 for the north shaft. To achieve this quasi-symmetrical design, even though the chamber is offset from the centre E/W axis of the pyramid, means the slopes of both shafts had to be different.
If the aim was to create a symmetrical design that 'targeted' a specific star, the North or Pole Star, Thuban in the northern part of the sky, and Orion in the southern part of the sky, then a bit of juggling with the initial angle of inclines of the slopes was needed, and a slight adjustment to the slope at the top end of the north shaft. The end result is an elegant design that accomplishes what may have been an attempt to provide the Dual king with several options for his celestial afterlife, realized by creating a harmonious dual shaft symmetrical design, reflecting his rule over the Two Lands.
CT