Help with total loss settlement

On March 22 my vehicle was totaled by another driver. Last week State Farm finally offered me $13000 total for the car, which I thought was fair. I signed and returned the documents. I owe $1100 on the vehicle and they made no mention of the payoff, so I thought it had been taken care of. It turns out, they forgot there was a lien on the vehicle. They called asking me for the title, and I reminded them Toyota Financial has the title. They are now sending me updated documents, with the amount of $11,900. I spoke with them on the phone and said I would now have to review the numbers and would call them back tomorrow. How can I negotiate to receive the original amount they offered me? It's been over three weeks since the accident and I did not get a rental car. I have been very patient and for the most part they have been very helpful, but $1100 makes a big difference to me.