To what extent is the placebo effect due to conscious expectations of the patient overriding the effects of ongoing cellular memory that is giving rise to symptoms in the body?

This can indeed be a factor. It is responsible for approximately 30% of the placebo effect. The other aspects are deeper interactions through the workings of the mind on a subconscious level to allow the deep subconscious some relief from its conflicts and torment, and this letting go will ease the karmic influences serving as a strong stimulus to cause discord in the body.