I'm someone who enjoyed STID more than most people seemed to, but there are definitely some things that could use some fixing. Consider me very interested in this edit.
Yes, get rid of the Khan references if you can. Dub in the characters saying "Harrison" wherever you can. If the lip sync doesn't match up, see if you can cut away to another character listening, then cut back to the speaking character.
Also, please get rid of the Old Spock scene, which is by far the worst scene in the movie, IMO, for several reasons:
1) "I have decided not to interfere with the course of events by telling you about the future. However, having said that, let me now tell you everything without any further prodding."
2) Old Spock saying that Khan is the worst villain they've ever faced seems like a bit of nonsense to me. The filmmakers were trying to fashion Khan into Star Trek's version of Darth Vader, Voldemort, or the Joker. But guess what? Star Trek doesn't have a villain like that because it doesn't need to. Not every franchise has to be exactly the same.
3) Having gotten the information from Old Spock, Young Spock promptly does ... exactly nothing with the information. Take out the scene, and the rest of the movie plays out completely the same way -- as good a reason as any for its deletion. If the filmmakers had Old Spock give the information to Kirk -- if Kirk knew that originally, Khan killed Spock, so Kirk chose to sacrifice himself in his place -- the Kirk-death scene would have been loaded with dramatic irony and emotional resonance. But that's not what happened.
Anyway, are you thinking about using an alternate subtitle for your edit? If I could just throw one out there, I think The Seeds of Wrath would be cool, since the story is a mashup of "Space Seed" and "Wrath of Khan" (even though we want to remove the direct reference). And within the context of the story, the title would still make sense: We learn about the events that lead to Harrison's wrath. Anyhow, it's just a thought.
Whatever the case, I look forward to learning more about this!