Um...I'd have to disagree with your definitions. For example, the theory behind some powerful abilities(I'll use Professor X for an example) is still enhanced something. His mind is simply enhanced to the point where he can read people's minds, or even control them.
What about Flash, wouldn't he technically only have his speed enhanced? Yet I would certainly classify that as a super power. How about a cyborg, or alien whose race gives them extra abilities over humans?
Anyway, I would suggest one of two things: (1) remove the part about super powers. The Immortal rule would still remove those like Superman, Wonder Woman, Galactus, etc. It would allow certain others in that you mentioned, but if you don't like that, then do number (2) tighten the rules about super powers. Something like...no genetic modifications, only skills. True, this would exclude Wolverine, but honestly...he has super powers, he shouldn't be allowed.
Your choice, just my thoughts.