I wouldn't wait until the project is completed. You can insured projects at different values while your car is under contruction. I have a $2500 policy on my Studebaker.

More than one garage has burned down with an uncompleted project. Hagerty is good. Other companies that can give you a competitive quote are Grundy, Great American Classic Collector, Foremost Antique Auto, and I sure there are others. Foremost is underwritten by Zurich and Great American's by Infinity.

Make sure to keep the amount the car is insured for up to date while the is being constructed. If you just installed that $10,000 engine, make sure you see your agent.