When you mentioned “competitive private” in CT: Do you mean like Hotchkiss or Choate? As others point out above, many of the private high schools have well connected college counselors. They can give you a good estimate.
Where would you estimate your 3.68 ranks in your class? You can get an estimate from Naviance or SCOIR. If you’re outside of the top 5%, its a slim chance in RD (unless you are URM, development or USMO Gold medalist).
Have you considered Imperial College London?