April offers the Klingons the Enterprise in exchange for being governor of Phadeus IV. Where's April's leverage? Like the Klingons wouldn't double-cross that agreement? April wouldn't know that? It's stupid.
How in the world would the codes April knows work on the new Enterprise twenty years later?
There's certainly nothing in the story that hints Harrison is Khan. Why would Khan have a dog in this particular fight? What vengeance would he be seeking based on what happened on Phadeus or to any of the other characters in the comic?