https://www.sciencedirect.com/science/article/abs/pii/S01918...
TL;DR: Yeah, powernapping is a thing.
In the past I tried various different times ranging from 6:30pm to 9:00pm. Even taking it at a suboptimal time is better than not taking it at all.
There are also a few other things I do to keep my sleep schedule on track:
1) I heavily use bluelight filters on my computers and phone in the evening. Redshift/gammastep on Linux gives me full control.
2) I have low blue light lights which I use in the evening [0], then I switch to fully red bulbs in the hour before going to sleep.
3) I have a super bright daylight LED lamp which turns on automatically at 8:30am, a few minutes before I wake up. This is my solution to automate light therapy [1].
All of this combined lets me function mostly like a normal person. Hope some of that helps.
* Adjusting diurnal rhythm (e.g. adjust a skewed sleeping schedule, jet lag). This works in lower doses over longer periods of time. So if you want to be less of a night owl, you may take 0.1-0.3 mg in the afternoon.
* Hypnotic - immediately making you more prone to fall asleep. This one is less well understood and dosages vary per person but it seems like 0.3-3 mg shortly before bed time is optimal. It also won't work on it's own like stilnoct or whatnot, so limiting light exposure, and all the other usuals, still apply.
I also find it frustrating how much more expensive and less available lower dosages are. From someone who also does bits and nibbles of 3mg pills.
1) The proper dose of melatonin for me is somewhere between 150ug and 400ug, but most melatonin sold comes in 3mg to 10mg pills. That's around 10x too much, taking that dosage of melatonin destroys my sleep schedule. It takes a lot of hunting to find the right dose. I tried once to crush up some melatonin and make my own pills with a precise dosage, but that ended up being a bit of a disaster.
2) Melatonin is regulated as a supplement in the US. Basically that means there is no regulation and even the active ingredient can vary wildly in a pill. When I visited a sleep specialist they mentioned to always buy the same brand, because "Each supplier has a different incorrect dosage, your best bet for dialing in on the correct dosage and timing is hoping that they're at least consistent among themselves".
But I do agree with you, regulating it as a prescription medication would do more harm than good for most people. I wish there were some middle ground that would both solve the above issues but still keep it easily available for people who rely on it.
[0]: https://en.wikipedia.org/wiki/Delayed_sleep_phase_disorder