So where did all the fresh water come from to sustain the sizeable workforce required to build such a structure if, as you say, "The Nile had many stagnant backwaters that were full of nasty things and the river itself was laden with schistosomiasis and was foul during the spring." I am assuming that the workers were not just drinking alcohol which you presume most of the Nile water was turned into so that harmful bacteria were destroyed - the precise building measurements suggest a sober workforce.
The workforce did not have access to a supply of freshly pumped water as the pump hadn't been built yet and therefore could not be operational.
It just doesn't add up to me. What am I missing?