I've heard that keeping your neck warm (use a warm/hot towel perhaps) can help with whiplash. If you want to try this, don't delay. I think the heat helps to settle the neck muscles down and help them heal. This is just what I've heard on the grapevine, not AFAIK standard medical advice.
As for the insurance, a lot of people used to think a third party's insurer couldn't write off your car, but I'm not sure if that's correct. The old guy's insurer will probably offer you a sum of money to write the car off. This is usually a low figure, if so be prepared to get evidence of how much a supra will cost you to buy, and begin the haggling process.
I'm not sure if your agreed value with Livingstone will take effect because you won't be claiming on that insurance.
I've probably raised more questions than I've answered, but hopefully they're good points to consider.