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.
Remember though, professor X developed the powers on his own, that is not classified as a Bio genetic enhancement because they came naturally, Wolverine is a good example of a biologically enhanced being because thats just what he simply is, he never grew these powers on his own, although i still may have to exclude him since i only said "slightly", he has a heavy modification so I guess he is too much.
Flash is classified as Super power aswell because he was not genetically enhanced by someone else but by something which were some super charged atoms of a radioactive liquid that gave him his powers.
but You are right, I should tighten them up a bit.
MODIFIED RULES FOR THIS BATTLE:
No immortal or celestial beings, NO POWERS, only skillz. (ex: Batman, Green arrow, The Punisher, etc.)