Apart from considerations of courtesy & safety, notifying the endocrinologist properly and in advance of your intention to start a different regime of delivering the dose, might mean that the effect can be measured and added to the "sum of knowledge" about CAH. Otherwise, isn’t it likely that your potentially valuable case study might be filed under "non-compliance"?

P.S. I never thought I’d be discussing "The Rhythm Method" with some ladies I have never met!!