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My background is physics and during an extended beer session my group talked extensively about what properties an interplanetary time keeping system would need to have.

The answer we came up with was: thank god we'd be retired or dead by the time it became a problem that we had to deal with day to day.

You would need something like international atomic time to be the basis for it, but unlike TAI which is the weighted average of some 400 atomic clocks on the surface of the planet, you would need to define it with respect to free space (which we can't access) and with respect to a single event that's accessible to everyone yet human scaled enough that it happened in written history (the best we came up with was the first nuclear blast).

Then you would need to have a calculation that turned it into local time which would be completely decoupled from any actual time keeping. Think printing the result of a square root in Roman numerals vs trying to do the calculation in Roman numerals.

Unix epoch is laughably inadequate for anything like that. Basically we have nothing today and you'd need an international agreement to have a sane time keeping system going forwards.