Thank you for mentioning the Babylonian side of this debate. Jens Hoyrup and Joran Friberg are free, as are others, to suggest what they will, and how they will, concerning the numerical foundations of Babylonian mathematics.
Having not read the Babylonian texts to the extent than they have, I will not enter into a serious debate with their views concerning the rational number relationship of Babylonian arithmetic and geometry as related to other Babylonian scribal methods and practices.
Where I draw the line is the vague suggestion that Babylonian views on arithmetic and geometry formed a fundamental basis for Egyptian geometry, possibly as early as the Old Kingdom, and therefore Egyptian arithmetic (using Hoyrup's model) very early included Babylonian geometry as a building block.
The Egyptian texts that I have read show, by Demotic script, post 1500 BCE, that Egyptian and Babylonian methods were different, and each culture's view and use of geometry did not change after wide debates and sharing of foundational information had taken place after 1500 BCE.
That is, my view is that, Babylonians continued to round-off all their rational numbers within their base 60 arithmetic, and oddly did not taken on any of the exact arithmetic features of Egyptian rational number arithmetic. Babylonians continued to round off their limited views of rational numbers through out their history, a fact that may allow Jens and others to fairly suggest that irrational numbers, found by their square root, and other methods, were real to Babylonians, 1,500 years before Pythagoras allowed Greeks to accept Babylonian advise on the topic.