I must say that I very much agree with the gist of your analysis. The remen and double remen (ie. 5 palm and 10 palm) divisions of the royal cubit are evidence of the square root of two approximations that were clearly in use at the time. (See Griffiths "Notes on Egyptian Weights and Measures", PSBA XIV and XV). In addition, if one takes the average of these 7/5th and 10/7th relationships one arrives at the 99/70 approximation you speak of.
In regard to the other points you have raised, please see my reponse to Milo's 10/5 message which I have just now posted. It will save me the time of restating things here.