Take your car to CARMAX and have them make you an offer. CARMAX will buy your car outright regardless if you are buying from them or not. That way, you'll have cash in hand to go with a new car loan.
By selling it to CARMAX, the BMW dealer won't be able to play around with the trade in value of you old car and purchase price of the new car. The more you try to reduce the price of your new car purchase, the less they'll offer you on your trade in... Better to have just one deal to be done on the new car purchase.
My speeding isn't the problem. It's the Slow Folks ahead of me that cause accidents!