The vast majority of rods are never destroyed in shop fires, accidents, or other disasters, never stolen, and never involved in collisions. But in the real world, stuff happens and someday you might have to make that call. As with everything else, every company has a little different approach. Some insurance companies recommend starting with the shop's liability coverage first and then filing a claim with your specialty car company. Others recommend going to your own insurance company first and letting them follow up with the shop's insurance if the shop is at fault. Make sure your auto appraisal is updated whenever you have added a significant value to the your project.
In the old days, hot rodders making a claim were sometimes unhappy about insurance companies dictating which shops they could go to for repairs to their damaged vehicles. Those days are over, as most of the companies allow their customers to work with the shop of their own choosing, so that you go to the shop where you want to have the work done-probably a place that knows you and the car.