Contrails do not vanish within minutes, due to the super saturation of water vapour in the air (especial in coastal regions) the rapid condensate can stay for hours or even days as there is a maximum amount of water vapour that can be contained within a volume of air. If the air is at 100% humidity then you would need to heat water exponentially to vaporize it. So no contrails can survive long times in the atmosphere. The hazy cloud cover you describe is the exact prediction of contrails in high humidity as contrails will condense to clouds but due to the high humidity the dust particulates will grow into a fog