Scott,
The big issue lies in that you must settle the existing finance and take out a new agreement when you part exchange your car. If you owe £3500 more than the car is worth then this must be added to the price of the new car.
Finance companies will probably not lend someone £6500 for a £3000 car but lets say they would for the point of the exercise.... Then, once you have been loaned the 6 and a half grand, there will be interest to pay on it bringing your total amount payable to, let's say, £9000. You will be increasing your amount owed by doing this.
There are 2 ways that I can see as being your ways out...
1) Personal unsecured loan, it'd have to be a cracking rate for it to be worth it.
2) Exercise your early termination rights - if you have them on the current agreement (dig out your agreement to check).
I hope this has helped you to understand what the hell is going on here.
JJ
You gotta tie yourself to the mast my friend, and the storm will end.