This implies that if you simply move time zones sufficiently then your natural cycle would match up with your work/life sleep schedule. Does that actually happen? If not, what other frame of reference is your natural cycle syncing up with?

A lot of biological processes are kicked off by light exposure, and by "number of hours of light exposure".

For example, the change in an animal's coat type (summer vs winter) is triggered by the number of hours of sun they are exposed to. Once the days get shorter, the summer coat falls out and the winter coat starts growing in.

Presumably that means someplace your body has the equivalent of an accumulator running measuring hours of sun exposure. :-D (This is also why people deprived of light, or exposed to non-stop light, quickly find a lot of their body's rhymes get way out of wack.)

Anyway AFAIK that system is part of how we adjust, eventually, to changes in time zone.

A lot of other things in our bodies are cyclical throughout the day, month, and seasons. Including men's hormone levels, with testosterone "peaking in October and ebbing in April" [https://www.apa.org/monitor/2011/03/hormones#:~:text=Men%27s....]

I guess my TL;DR is that we're still animals and we can't logic / alarm clock our way out of biology.

Light. Especially sunlight, the exact effects of artificial light are not completely clear (or rather, it seems to have an effect, but it's not completely obvious which parts and how: this is part of the theory of why avoiding blue light in the evening can help with sleep but it's not actually been demonstrated that it works as an intervention).

People's daily clock is naturally (i.e if kept in a dim light constantly) slightly longer than a day (exactly how long varies by a few hours), but it becomes synchronised to changes in light level (there are actually specific light receptors in your eyes that do this, independent of vision). Exactly what 'phase' this clock has compared to the change in light levels varies from person to person, and throughout their life. There's a decent body of evidence that teenagers naturally shift towards being more delayed as they go through puberty. There are even disorders where it can become very far out of whack: people who will want to sleep very early or very late, or in the most extreme case (usually people who are totally blind in a way that also disrupts these specialised receptors, but also some people who have functioning sight), where the synchronisation doesn't work at all and their natural sleep cycle will drift freely with respect to the day-night cycle.