If someone works the night shift and wakes at 8PM, should they take their first sample at 8AM? No, cortisol levels follow your diurnal rhythm, not the clock. The first sample is your waking sample, not the 8AM sample. The others are regularly spaced through your wake cycle:

wake
wake + 5h 20m
wake + 10h 40m
wake + 16h

But this is if you have a regular schedule (with a wake cycle about 16 hours long).

If you don't have a regular schedule, it's hard to know what your cortisol levels will be. They may be all over the place because your body doesn't know night from day. And, yeah, that'll screw up your cortisol test results. But, think about it. Your results are bad because your cortisol levels are bad. So the test results will probably reveal that your levels are odd versus what they should be for those times of (your) day. And it seems likely to me that your levels will probably be in flux, so your results may only accurately reflect that particular time you took your samples, not the week or month after, or generally. It may make sense to try to get your sleep more regular before performing diurnal cortisol testing.

Even without figuring out your over-the-day pattern you may still be able to get meaningful results from a whole-day test. I believe there are urine collection tests that aim to measure your daily cortisol output. That might still make sense at this point for you.

Things to help with sleep:

Regular routine, quiet environment, low lighting, no blue lights, no stimulants during the day. Melatonin half hour before bed. 5-HTP before bed (if not taking SSRIs or at other risk of serotonin syndrome). Um, those are the things that have worked for me. I can't think of other aids.