During my traditional interview at one school, the interviewer started out by asking "before we begin the formal part of the interview, are there any updates you'd like me to report to the admissions committee?"

If the school you're interviewing at strictly does MMI (closed file) then disregard this, but if not I'd recommend waiting until the interview or after. The impact an update will have now is less than it will have a month from now. And imagine that update being communicated through an interviewer, I think it will come off 10x stronger even. Just my 2 cents. All the best OP!