Don't forget vasopressin, also very important for sleep stability/fragmentation and I'm guessing GH probably affects it's release, receptor expression, ... if nothing else, via increases in plasma osmolality due to increased sodium retention ... : D
I'm not going to pretend like I know the answer to this, as I don't think the science community has a clear understanding of it, but anything that increases sleep pressure should help. Although any agents in this regard will have a noticeable effect on your brain chemistry (think sleep medications like H1 antagonists which increase SWS, ...) and overall mood/cognition.
For me, most of the awakenings happen during REM, so if I was to base my hypothetical over my personal experience I'd go in the direction of decreasing REM density (5HT1a agonists do this, for instance CBD) or maybe vice versa, increasing REM stability, make it harder to wake from REM (cholinergic's, I had success with phosphatidyl serine, although combining two drugs which make REM sleep more vivid might be a wild experience).
Also seeing how GH increases NREM2 and decreases SWS, anything that increases SWS should help. But now we are again at H1, 5HT2a antagonists, pregabalin, etc. GHRH (ie. cjc1295) which increases SWS might be worth a try. Maybe dual orexin receptor antagonists? but purportedly, they also tend to increase REM ...
In regards to cortisol I'd potentially try some natural adaptogens like bacopa or ashwagandha, rhodiola, as mentioned phosphatidyl, etc. But everything here will again have an effect on your mood/cognition and I'd be weary of ashwagandha.
One thing which is for sure is that what ever will down regulate/calm the HPA axis and the amygdala should help (providing that some deficits aren't the issue in the first place) as GH related sleep issues are most probably more prevalent in people who have problems in this department already. I'm talking about taking care of anxiety, stress, etc. It takes about 3 months for the HPA axis to normalize.
https://www.embopress.org/doi/full/10.15252/msb.20209510 A hyperactive HPA axis will fragment your sleep as is and will react with a greater intensity to any agent which has an inclination of modulating it, GH being such a substance ofc.
Maybe there is a protocol out there which doesn't include the use of such psychotropic drugs, if so, I hope someday somebody finds it. I'd look at electrolytes and blood glucose management first ... I personally found that I was sleeping even poorer when sodium ingestion was higher for instance.
