There are steroid calculators out on the Internet and they are very useful.
A normal body has a peak of cortisol in the morning and declines all day. With a short acting steroid like cortef or hyrdrocortisone, you can mimic a normal body. Prednisone and dexamethasone act much long, 36 to 54 hours approximately.
That being said, there are pros and cons. If you have another disorder that needs to be treated with a bit of steroid, then the dose needs to be up. If you are just replacing, then you are just taking a smaller dose (usually 5mg in prednisone).
He may also need other medications like something for blood pressure, other hormones to be adjusted etc. I suggest you find an doctor that will take some time with you and get copies of his test. He may need more salt in his diet.
Try a larger hospital or university. Find a neuro-endo.