Unfortunately once you signed the paperwork with BMW FS saying you agreed to the terms, you were stuck with those.
Paying the car off in full and taking out a loan really isn't a great idea either. You'll probably keep a similar monthly payment, but depending on your payoff amount you'll most likely now be stretching out that payment for an additional 5 years.
With that amount down up front you probably should have been closer to the low $400/month. I'm guessing you ended up paying the full MSRP for the car, all of the fees, and had them bump up the money factor/interest rate on top of that. (Not sure what the money factor was when you bought your car).
You're probably stuck in the situation, you're young enough where you can use this as motivation for understanding all the lease terms for the next round.
Current: '15 M235i Vert
Previous: '13 335i, '08 TL-S, '00 Corvette