jujoules, please refer to other posts (particularly by Spayurpets) that question Demosthenes’ position about LSAT/GPA requirements.
I wouldn’t see a need to get an MA if you have a 3.67 GPA and a strong LSAT score. You should be able to get into a few of the top 10 schools.
Your analysis of private international law is accurate. I don’t know much about public international law, other than that positions in it are few and far between and don’t pay particularly well.