What's your average no-insomnia length of sleep?

The key to being rested isn't the hours, it's the minutes. Because it's where you come out of sleep in regards to your brain cycle. The goal is to go into waking from as close to REM sleep as possible.

So, for example, since typical sleep patterns run on a 20-40 minute cycle (that's REM to deep sleep and back to REM), if a person is complaining they aren't waking up feeling rested I'll recommend adjusting their sleep by ten minutes, so that regardless of what direction they shift their pattern it puts them closer to REM.

I would recommend the same here. Maybe add an extra hour to your normal number if you can. And make a point to keep what your average sleeping time would be. (So if you work nights and are normally sleeping during the daylight hours, maintain that.) When your body switches its sleeping/waking rhythm it can feel worse than just having insomnia. This may mean you'll need to force yourself to stay awake the first day so you go to bed at the right time.

Also, I know you said no recommendations for medications, but in the regard of ensuring you're going to sleep post-insomnia, take some melatonin just to coax the body into wanting to go into "sleep mode".