If you trade the car in now you will realise a much larger loss. As this situation was not self emposed, it seems harsh that you should be out of pocket. I'm not sure how old your car is, but I would guess that you would have to put £6-7K to it to buy a new equivalent replacement.
I'm not sure that it will flag up as stolen/recovered. I think that would only apply if you had been totally paid out on the car, then it was later recovered and sold at auction by your insurance company.
If I were you, I'd stick with it and don't let the bastards grind you down.