If your mentor is a top professor at Rutgers, then s/he might have some influence on admissions or be a member of the admissions committee. Would you feel comfortable contacting this person to discuss your concerns? If you have maintained contact, you could just express your strong interest in the program and the fact that you were disappointed in your GRE scores, you want to apply, but don't want to hurt your chances of being accepted. And, just ask if s/he would recommend applying this year or waiting until you can retest.
I would guess that the professor will recommend that you apply. The advantage of contact is that you get to show how interested you are in the program, sort of explain the low test scores, and put your name in the professor's mind.
Really, don't distress too much about scores. I know it's disappointing, but everyone has good and bad things about their application. And, you have a lot going for you. You have a solid GPA, good recs, and great publication experience! I think you have a really good shot. We'll be rooting for you! Let us know how it goes.