I'm quite interested in this idea of comparing distance measurements from Cook's voyages with modern values because if modern methods are reliable and difficult to refute across the globe then calculating the length of a degree of longitude north of the equator, on the equator and south of the equator should be simple. And if it then turns out that a degree of longitude is shorter anywhere south of the equator than on the equator, then there are consequences, because as Rowbotham (Earth not a globe) says:
"The following is the true state of the question:--If the earth is a globe, it is certain that the degrees of longitude are less on both sides of the equator than upon it. If the degrees of longitude are less beyond, or to the south of the equator, than upon it, then it is equally certain that the earth is globular" (my emphasis)