There are only two things that make me think that Harrison is just not a straight up Khan 2.0:
1. Khan had North Indian ancestry in the original timeline. But, could be a loophole to that. Take a look at what wikipedia said:
In "Space Seed" writer Carey Wilber's original plot treatment, the character of Khan was a Nordic superman named Harold Erricsen. The first draft of the script introduced the character as John Ericssen—
Would they break television canon? Of course they would.
2. The film Cloverfield was long rumored to be a Godzilla or some other legendary monster film. Cloverfield was said to be a "codeword" Of course, we all know that ended up being the actual name of the film. J.J. Abrams misdirected by not misdirecting at all.
So, what I am really trying to say is maybe John Harrison is John Bon Jovi. After all, he is Wanted....Dead or Alive.