Coats of many colors

As mentioned earlier, we have found many colors on this 46 year old car, depending on what part of the car you look at. We know the original color was Wimbledon White, and including in no particular order, Yellow, Orange, Red, Green and Blue.
In conversations some people have advised the project will go much quicker if we just paint over everything, but we want to know that we have done it right, in taking it down to the bare metal, having all proper body work done, and having a professional apply the primer and paint.