If we are going to present Unix Epoch in a reasonable manner, do the following:

YYY/MM/DD HH:SSS

SSS is seconds from 000 to A23 (only use of alphanumeric). This gives you an amount where the next unit of "hours" is 2^10^ seconds, or ~0.28 hours.

HH is "hours" from 0 to 63. This gives you an amount where the next unit of "days" is 2^16^ seconds, or ~0.76 days.

DD is "days" from 1 to 32. This gives you an amount where the next unit of "months" is 2^21^ seconds, or ~0.81 months.

MM is "months" from 1 to 16. This gives you an amount where the next unit of "years" is 2^25^ seconds, or ~1.06 years.

YYY is "years" starting from Year 0 in Unix Epoch Time.

Expect that few people actually keep time this way unless they are forced to. Likely, the only people doing so are militaries that routinely have to coordinate with other militaries where a dominant time can't be agreed upon.

There could be an adjustment with the binary hours and binary days to get binary days close to terran days since a binary day is only ~18.2 hours long and that could be an issue with running a ship.

@HobbitFoot @econsa
Once you are working over distances where the speed of light starts to really matter, there is no "Earth UTC", no "what time is it right now on Earth?" because there is no "right now" that isn't right here.

But yeah, the second of relative time is an SI unit with a physical definition now; that's staying.