It seems the consensus is to change the wording to be geared towards editing the current question, rather than asking another. I propose the quote should be:
This question has been asked before and already has an answer. If those answers do not fully address your question, or if your question is actually different than the duplicate, [please edit your question] to be more clear and allow for it to be reopened.
For the part surrounded with brackets [ ], I think it would be a good idea to link it to the edit post page for the question.
I asked this question on Meta Stack Exchange since I was told by Moderators that they cannot implement this change since the message is an SE wide feature, and it turns out that depending on the ownership of the post, you see a different message here. For the person who posted the duplicate question they see this:
So, if your question is closed as a duplicate, the closure text already states to edit the question.