Hope things have improved since you posted!
I have only just been diagnosed with ADHD, so I can’t speak to drug side effects, but I have been fighting the good fight with ADHD sleep my whole life, and here are my top two tips:
Melatonin doesn’t help me. I only take it when there’s been an interruption of my circadian rhythm (jet-lag especially, but if a new med is keeping me from sleeping, I do find it helpful to “reprogram” my sleep cycle by taking it every night at the same time for a few days/weeks).
Before bed, I take some powdered Cal-Mag-Citrate, dissolved in water (available on Amazon or at compounding/natural pharmacies—I have not had success with pill form). Years ago, someone tipped me off to it, but I’ve never understood why it helped! The quality of my sleep is DRAMATICALLY improved when I take it, so too is my awake time. I understand the science better now, and the short version is that it’s that magnesium that allows the brain to do its best nighttime repair work. The calcium citrate helps your body use it. Now, I just have to figure out how to sleep through a full bladder after all that water before bed!
Get some rest!