I am a parent who was on the other side of your problem just a few years ago. An article was recommended to me and I am posting the link here for you to read and then print for your parents. The Peabody website (in the Admissions section) has a couple of other articles that may interest you as well and is a good resource.
This one is titled: "What Can You Do With A Music Degree" Peabody Institute - Conservatory Admissions: What Can You Do With a Music Degree?
This was very helpful along with the fact that I know a number of music majors that have gone on to not only have careers in music, but also those that chose to attend either law school or medical school down the road. The one thing that my musical friends have in common is that they are all very intelligent. So your case about the 4.0 and ranking fit with this trait that is quite common among musical people.
Something else that I found interesting was when I went onto my S's Naviance system at school, the average gpa/test scores for those that went to conservatories was above 3.9 and above 2150 SAT (we have a very large music program.) Again, a confirmation that music major students are hardworking and intelligent.
So your desires are actually the way you were built. It is up to you to decide how to use it, whether continuing to a career or finding some part of that experience that will make you who you are down the road. We embraced S's desire to pursue his path completely understanding that it is he who will decide his future and make his own way.
One final note - we know of a young woman that was in your position (4.0uw/ranked 1 and a NMF) She desperately wanted to pursue music and was accepted to many top music programs. She was offered a full tuition scholarship to a small liberal arts college and her parents basically told her they would not contribute a dime to a music degree. Reluctantly she took the full tuition scholarship and went off to major in Math/Science.
At the end of freshman year, she came home, took her family and music teacher (my S's teacher) out to lunch and announce that she had changed her major to music. When her parents saw how happy and determined she was, they accepted her decision and today she is working in New York writing and performing in musical theatre. Something S's teacher said to me a long time ago and as a parent of a musical kid had a great impact - "you can force someone to follow another career path but you can never take music out of their soul."