Basically, in ME politics, there almost always seem to be three players in the mix. An authoritarian military, secular democrats, and the Umma.
If they could find a way to corral the defence and religious elements of the conversation, then the argument gets to be about economics and other matters.
But with obedience to Islam as one factor in every discussion and the opposition of the army to the loss of its status, the whole discussion happens in a strange place from a Western viewpoint. We had our secular enlightenment long ago. Our defence forces accept a role as protectors rather than rulers of the sovereign state. We don't have to deal with these questions. History provided an evolutionary pathway for us.
I think the only way to keep the military folks in their box and the religious folk in their box is to corral them both in an upper house of parliament. By conceding influence and prestige to them without granting them a veto.
But can Egypt reach that sort of accommodative journey's end? I am not sure any of the actors has the nouse to write that kind of constitution.