When re-imagining an existing character, what role does the writer
have in trying to find balance for both new and old audiences?
Now, that said, when dealing with the task of re-imagining a character, my belief is this: You have a responsibility not to tarnish the legacy of the original while taking it to new readers in a way that rings true to the basic, core understanding of that character.
What does that mean?
To me, that means that if your hero is a genuinely heroic character and your re-imagining is a darker character struggling with being heroic but wanting to ultimately, you're treating the property with respect. If, however, you write the character as a phony who only pretends to be heroic for some ulterior nasty reason, then you're altering the core and only keeping the name of the character.