I have done two of these kinds of test. You are spitting in a vial four times during a day, right? First thing in the morning when you get up, before you eat lunch, before you eat supper, and before bed? Make sure you have a clean face, no lipstick or gloss to get on the vials. Follow whatever directions come with your test. If you are not having a period, it may not matter what day of the month you do the test, but if you are, then it does matter and you would need to find out about that. (I know you said you have missed a period, but do you regularly miss it?)
Also, it is my opinion that consuming stimulants will skew your results. Caffeine and Sugar raise cortisol levels. If you are drinking coffee all morning and then spit in the vial before lunch, your cortisol levels will appear higher than they normally would be because the caffeine is pumping your adrenals. Then your doc will look at the results and think your cortisol levels are higher than they really are. If I were you, I'd try to lay off of the stimulants until the test is over.
I would not worry about the sleep cycle so much. It can takes weeks to establish a new sleep cycle. Just go to bed around a fairly normal time the night before the test. If you wake during the night, try to get back to sleep at some point. Do the morning spitting after you get up (follow what the directions say about your specific test) and go on with your day, spitting at the appropriate times. The tests I did required an empty stomach.
I hope you get some help if you think you have adrenal issues. I wish I had listened to a friend about 17 yrs ago who tried to tell me how important it was to always support the adrenals. I poo-pooed the whole thing and wondered what adrenals even were!! Now I know all too well. One thing, don't think the situation will get better all my itself. You will have to be pro-active in making sure you live a healthy lifestyle, take supplements that support your adrenals, eat healthy food (organic if possible), don't live a wild life, get plenty of sleep, lay off the stimulants, and try not to stress over the little things in life.