I found it was possible to remove from vicinity inventory but I had to stand in weird positions like; at the back of the car to remove the engine parts, and on top of the car to remove front wheels/hood.

I had this exact thing happen to two cars. First one, was ADA 4x4, and it occured exactly as you described, lag spike, crash and can only remove the battery which wasnt ruined. The ruined parts that cant be removed are the hood, front two tires, spark plug and radiator. The car has an orange check engine and has not despawned through server resets. I have checked this car after 2 server resets, no change.