No, unfortunately the insurance companies aren't usually interested in repairing a vehicle when the repair costs are so close to the total value of the vehicle. Usually (in my experience at least) if the cost to repair is greater than 50% of the value of the vehicle they'll total it out rather than repair it.
According to your information and KBB the value is ~$13k, and the repair costs are somewhere around $11k. They're not going to do that, especially when the salvage value of the hulk is only around $7k. Your best remaining option is likely to turn in any receipts for recent significant work you've had done to the body or drivetrain. Sometimes that will increase what they'll settle with you for.
Good luck with it in any case.
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