You aren’t delusional; you are a strong candidate and applying ED gives you your best chance. Even with that, it is still going to be a reach, and I think you understand that.
Unless it is a very compelling story that really ties together your interests or involves research etc, I don’t know that explaining whatever non-legacy connection you have with the school will be helpful, it feels like walking a fine line. Applying ED shows it is far and away your first choice, you don’t need to overdo it.
Make the essay as good as it can be and see what happens!