Harvey, what you describe is how I have approached it so far, but with only so-so success, including in oak. As you say, this is the battle of moisture and tension. What I find interesting is that producing very thin material, like 1/8″ or less, is easy because cupping usually doesn’t matter and usually isn’t very much. For 1/2″ and thicker, the cupping is usually minor, I think because the material is rigid enough (thick enough) to resist the changes in tension. But, at 1/4 to 3/8″, roughly, it seems quite challenging. My theory is that the material is thick enough to build up a fair bit of tension but not thick enough to resist.
I have a 14″ wide piece of 6/4 walnut from which I must obtain 10″ wide by 20″ 3/8″ stock for the sides of a clock. This material is flat sawn. Buying quarter sawn to yield 10″ in walnut isn’t an option right now, patly because of cost and partly lack of supply.