I think they should have BOTH Shazam and Black Adam in the story but as the same character slot...
Look at Sektor and Cyrax in MK9 they added both human and cyborg forms and they had different voice actors,
intro, finisher and victory cutscene. Your finisher idea is great for Adam, while Shazam should just do the grapple/shouting move...
The Character should have magic punches as gimmick to have more damage and they should do lightning shooting and
lightning bolts throwing like Superman has heat vision and cold breath.
Adam's voice should be dark sounding while Billy sounds more childish and that way they could both have there spot in the story
but as one character, ofcourse the name will be Shazam cause Adam is costume 2 but in the end of the day they're both the champions of SHAZAM!