Does this school even take and consider LOIs?
Usually mentioning another school is only useful the school you are currently accepted at is ranked higher than your dream school and you are willing to give up the higher ranked school for your dream school. Which doesn’t seem to be the case here.
Has your article that you plan to publish within a month been accepted to a journal?
I think you have plenty of time to d write a LOI. And as is frequently stated here, most of these letters are simply filed .
With your current results, you seem to be having a great cycle. No matter what happens, you are going to be a doctor. Congratulations.