I don't believe that F. Scott Fitzgerald could have changed the end to The Great Gatsby and still had the same effect on the reader.
The story is a tragic one where reality and idealism battle for supremacy. The characters in the story exist more in a world of illusion than of reality. For instance, Jay Gatsby is living with the idea of Daisy five years after they first met. In his mind, she has not changed, and he acts as if they can pick up where they left off, even though she is now married. Daisy lives in an unrealistic world as well, believing that she can somehow have a real relationship with Gatsby without leaving her husband.
Tom has an affair with Myrtle, but Wilson does not seem aware of it, believing that Gatsby is having an affair with her. The plot is driven by wishes as to what could have been, rather than the truth of what life has become for these people.
Had Wilson not killed Gatsby, I believe Daisy would have stayed with Tom, who would have continued his relationship with Myrtle. No one seems to be aware of what they have or what is at stake as they lead foolish lives. The cycle would still have continued in some fashion and no one would have found the satisfaction they hoped to find in their irresponsible behaviors.
Jay's only chance to be freed from this obsession of Daisy was to lose her completely: in this case, by his death. He shows no signs of being able to dismiss his unrealistic feelings for her, and doesn't seem strong enough to leave at his own volition—even though he is warned that he might be in danger since his car struck Myrtle, Jay refuses to separate himself from Daisy.
It is a tragic story, but I cannot imagine a way where the same feelings would have been generated in light of a different ending.