Will a 770 and a 3.8, here are two other possible issues:
1. They are afraid you will go elsewhere. I saw this happen once or twice where candidates with amazing numbers such as yourself didn't get into places they should be getting into. It could be that the Adcom looked at your profile and decided "Nah.. this guy will just get into Harvard... Were his sixth choice". so the way to adress this is in the extra materials you submit make them KNOW 100% that you REALLY want to go there! For your number one choice, let them know that you will definitely go if accepted and show them through specifics that you really think you fit.
2. Career/goal issues - this you pointed out yourself, and this can harm an otherwise excellent application. Hard to say without seeing the essays myself... but since you yourself identified it, you may be right.

anyhow the important thing to know is that its not too late! Let them know about your passion for the school, any other advancement and if you have any element that you neglected to mention or develop... but get that letter out there!