Engineering/music Major Chances

Hi all. Vandy is one of my top choices. I know Vanderbilt is a reach school for pretty much everybody, but I was wondering if I should even spend time on the application. Ideally, I am looking to double major in Piano Performance and engineering. If I am not accepted as a music major, I would still love to go as an engineer.

My stats are a little different as I home schooled for junior and senior year, taking classes at NC State university. Because of this my GPA does not really matter (you may say it is a little low). I have super strong EC and a decent ACT score.

uwGPA: 3.7
ACT composite: 32
Senior classes:
Calc 2 (NCSU)
Calc 3 (NCSU)
Physics–mechanics (NCSU)
Accounting (NCSU)
AP Macroeconomics (self study)
Business writing (my own curriculum)
Spanish Immersion (self study)

By graduation I will have 32 college credit (transferable). I took a very competitive course load at the high school I attended as well. I write pretty “fire” essays and believe my CommonApp essay and supplemental will strongly help.

EC:
-Founded/captained two FIRST robotics teams-both achieving the highest level, going to World Championships in St. Louis. I have been reconized for my work with STEM in the community by the local Towne Council. Raised over $40,000 for STEM education.
-Competitive soccer-multitude of awards including best in NC
-Founder of Community Tech Drive–collect unused technology in my community tor underprivileged students. Recognized by NC House Representative Tom Murray.
-Piano–multitude of awards, including multiple 1st place in top competitions.
-Honor role at the high school i attended.
-1st in state in CYBERPATRIOTS hacking competition
-Participated on high school ethics team-national runner-ups
-Founded a business: Not Ur Mothers TieDye (tiedyed socks)

What do you guys think my chances might be?
Thanks a bunch