The difference between you and the 'factory' guys is that you care for the car. I was a guide for plant tours, then a factory service rep for the dealers, fitting doors for example: at the factory the guys have large heat lamps on the car and either pound on corners with large rubber hammers/mallets or use pieces of nylon sheet to lift corners, or a specialty jack handle to twist the door to a proper fit (even after the car is painted). Dealers use 2x4s to twist doors as many cars don't have any hinge adjustment (or beyond limit). So I can only assume that in order to properly fit the bucket would be exactly the same process. Heat-up the bucket then twist it to the desired shape, fit.
Denis