Again, the exact words you say are a wonderful description of how the chemical potential of an electron in a solid is defined. (Besides the trivial exception that for electrons in solids, it's usually expressed in eV rather than kcal/mol.) The chemical potential is the partial derivative of the free energy with respect to the number of electrons in the solid. In fact I wrote in wording just like that at the start of the "electrons in solids" section.

Your main complaint now seems to be the introduction, not the two physics sections that I just rewrote. I did not write the introduction and I don't like it any more than you do. I hope you rewrite it, or else maybe I will when I get a chance. (I did, however, write the "overview" section.) -)