OP-First off start the appeals process. You explained your case well here, but how are your interview skills? Be as professional as possible as you try and achieve a positive outcome. You are too close to the target GPA to have them **** you over like that.
I support taking a wide spectrum of classes. Say you have a challenging major, balance that out with a more relaxing minor. You can have the minor GPA overcome any of those C's you get in a brutal major. 3.3 in major, 3.8 in minor.