Well, actually, that's not quite true about circadian rhythms shifting slightly day to day, and varying for the individual.  It is basically the same everyday, for everyone. 

Like you, I had been inclined to think that it changed slightly depending on when you went to bed, when you woke up, and how many hours you slept. But, then, i started to doubt that that was the case.  Mostly because every chart and every article refers to that same ~4 AM - ~ 8 AM window for rise in ACTH/cortisol levels. Since babies sleep such different numbers of hours than adults, and have such different bedtimes, one would think that those hours would be qualified, if it was all relative.  Or that there would be different charts for children vs. adults and, of course, there are not.

That's when I started thinking that it must basically be the same for everyone. And basically the same everyday.  At any rate, I did just ask our doctor about this, and he confirmed that that was the case. (One of his subspecialties within pediatric endocrinology is circadian rhythm, so i have no doubt that he is right.) Interesting, huh?

To continue that heating/thermostat analogy: If turning down the heat as the sun comes up---and turning it up, when the sun goes down---is similar to dosing with the natural rise and fall of circadian rhythm, then giving a big dose at night, and a small dose in the morning, would be like doing the opposite, i. e. turning the heat UP in the daytime, and turning it DOWN at night.  Doesn't make much sense, huh? 

And, let's look at what would happen, if we were to do that.  Well, it could get VERY hot when the sun is out---couldn't it---and you'd FREEZE at night. If you wanted the room back to 68 degrees, you might even have to open the windows, in the afternoon, to let in cool air (BIG waste of energy.)  And in the wee morning hours, with the heat down low all night, the house would now be freezing cold.  To get it back to 68 degrees, you'd have to REALLY crank up the thermostat, if you wanted the house to warm up quick.

So, yes, it would be POSSIBLE to get the house back to the temperature that you want, if you did it this way, but you would be making it much more difficult for yourself, and wasting a lot of fuel, in the meantime.  And all because you are working AGAINST the natural heat of the sun.

In a way, that's really what the "big dose in the morning vs. big dose at night" question comes down to.  The natural heat of the sun, as it waxes and wanes across the course of the day, would be like the natural rise and fall of ACTH. If you don't care about the size of your heating bill--- which in this case, would be the total amount of steroids that your child has to take in order to suppress ACTH----then I guess you could make the argument that you can get there either way, so who cares.  But, if you DO care about side-effects (and what parent, doesn't?), and you don't want to drive yourself crazy in the meantime---chasing after good control---then it would pay to work WITH, rather than AGAINST, nature.