What are my chances of getting into Harvard? (Brownie points if you give more tips!)

I agree that it is very difficult to chance without test scores. Whether you agree with it or not, test scores can be a limiting factor in selective college admissions. For Harvard, I would think a “good” score would be 2250+/1500+ SAT or 35+ ACT. Although Harvard is a great choice for pre-med (grade inflation, reputation, smart students to surround yourself with) - I would also consider other schools of similar caliber and some matches/safeties as well. Good luck!