food for thought: I had a partner in construction and he swore by this. At least once a week he'd mention it to someone while we were in a home doing a job, about your natural hair oils and how he only shampoos twice a week... it was one of his talking points lol. He was a smart guy though and I think it's good advice. You seem a little ahead of the curve too imo smallpond.
If you do try this give it a month or two. It takes a while for your body to get back to producing those oils. It will feel worse before it gets better.
I thought the issue was over-production of oils. If you shampoo daily you're stripping your hair of all oil and stimulating it to overproduce to compensate.
When you stop shampooing, your hair continues to produce a lot of oil and looks greasy. After a while it reduces oil production and all is well.
Not that I've bothered to look it up, but that was the process I had in my head.
Not using shampoo at all would also do your hair a lot of good.