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See if the insurance company will let you buy it back.
I did that with one of my cars and had my friend fix it and pocketed quite a bit of money. I think I paid them $500 to keep the car and they were happy I kept it.
That car is far from totaled in my opinion.
In some states that's illegal. Once a car is deemed totaled and given a salvage title, you cannot repair the car and sell it and, insurance companies won't insure it in those states. Some unscrupulous people do what's called title washing. They'll buy a salvage title in one state and register it in a state that doesn't recognize a salvage title to clean it off the title record. They then turn around register it under a different name and sell it in a state that would otherwise prohibit it's sale if the salvage label was still on the car...
Buy it back, turn it into a track car. Trust me, road racing is the most fun you can have with your clothes on.
Considering how much they will probably auction it off for and what all I would need to do to get it track worth I would definitely go another route. Miatas and LS motors are cheap