Good call--baking soda alone or mixed 50-50 with salt, is an excellent dry shampoo. Also, can be applied a few hours before a wet bath, giving it time to sit on skin for maximum effectiveness. It is a good deterrent too, when used as a powder before bed,
BTW, your post reminded me: Head and Shoulders is also awesome. Brand is irrelevant, but get the formula that contains piperazine. It is effective as a hair/body wash, and morg don't seem to build up a resistance to it. I only use it about twice a week, with no other exfoliation except dry skin brushing before bathing.
My philosophy is to strengthen my natural skin barrier by leaving the "dead" dermal cell layers as intact as possible. (Also, many hair conditioners provide a nice "top coat": it seals the skin barrier much like it seals the hair shaft; used at the end of a wet bath it also leaves you smelling nice.)