I think you are still trying to engineer a wood bow instead of just building it! You are working with a living, breathing material and not a static material.
If your stave was well cured it should not have checked on the back. If you are unsure that your stave is seasoned, a quick spray of shellac over the back will seal it to prevent checking and can be removed easily, if necessary, later.
During the winter, in most areas of the US, the R/H id very low. Wood will dry without being forced but if you want to force it, do what must be done to dry it without causing other problems; reduce it to almost bow dimensions, seal the back and ends and allow it time to dry before stressing it. Impatience kills more wood bows than not and leads to frustrations that will kill the next one.