I know that it's considered a soft factor. Grad school grades don't factor in to your LSAC GPA. It sounds like it's subjective for every school but probably not a huge boost.
> @goingfor99th said:
> Also, law schools seem to look favorably on philosophy majors. That's because it's a rigorous major with a lot of analytical writing.
I was under the impression major is a very minor soft.
This law school sample resume has a separate section for publications. Since you mentioned your resume is lacking and publications are a good soft, I would make it a separate section. http://hls.harvard.edu/content/uploads/2008/11/golitely-resume.pdf
You have an awesome GPA and a nice soft with the Fulbright. If you want T14 you'll need to retake. With a high enough score you have great chances at every T14.
Imagine how high you can score this time around if you put 100% effort in?