Ten things I would change/adjust/keep the same:
1) If Billy can't be "Captain Marvel", then I would have it that saying his name activates his empowered form, but saying it backwards de-powers him.
2) Replace "Wisdom of Solomon" with "Intellect of Socrates". Billy hardly utilizes Solomon's boon other than be smarter, and having Sacrates as the the stand-in firmly puts Billy into the Greco-Roman camp. Seraph, the Jewish equivalent of SHAZAM!, can have the wisdom of Solomon.
3) The Wizard would still be alive, guiding his replacement (i.e. Billy). In fact, I might pull the Elders aspect from the television show, where Billy can communicate with his benefactors.
4) Restore classic Fawcett City as a "time lost" town, from the 1940s, making it a preservation site. In fact, it had, up until the first Crisis, placed in suspended animation by Dr. Sivana's "suspendium experiment", which gone wrong.
5) Give Mary her own sextet of female goddesses/elders; make her Billy's half-sister.
6) I'd keep Freddy as a Blond. Yes, heresy, but it breaks up the Brunette aspect of the Marvel Family.
7) Black Adam would be the villain he should be, when he first encounters the Marvel Family. In modern times, his descendant, a Egyptian-American boy named "Theodore 'Theo' Adama", would inherit the power of Black Adam.
8) Billy is the leader of the Squadron of Justice in the 1940s. Later, he becomes a member of the Justice Society of America; later, still, the Justice Society of America Dark .
9) Billy would be the Champion of Magic.
10) Pedro, Darla and Eugene would still get their powers.
That's about that...