I appreciate that your interest tends more towards consideration of arithmetic methodologies, and I of course see the great value in this pursuit. All I wish to add is that in most (if not all) of the cultures you mentioned I believe there to have also been a tradition of empirical geometry at play - being utilized in conjunction with the culture's arithmetical modality.
Jens Hoyrup discusses this theme at length in regard to Old Babylonian mathematics in his Lengths, Widths, Surfaces (2002). His term for this is "naive geometry". The clear inference is that the two traditions (ie, arithmetic and geometric) are not mutually exclusive, but rather that one informs the other. Each being brought into use where, and as, prudent.
Joran Friberg's work, Unexpected Links Between Egyptian and Babylonian Mathematics (2005), makes a strong case for a similar joining of traditions being in evidence in the surviving papyri.