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There is no way to get acccurate time back without seeing the moon, taking a sight from a known position or seeing an eclipse of one on Jupiter's moons.

The Sun could be a source.  It moves against the fixed stars at one rev per year, so it's a factor of 12 or so worse than the moon for accuracy.  There's also the dynamic range problem of measuring the Sun against the stars---since it is so bright, you need some sort of intermediary like a bright planet or the Moon (the positions of which need not be known as accurately), or perhaps a hack watch could help out with using twilight as a bridge if no intermediary is available and you're desperate enough to want to use the horizon with its large refraction uncertainty.  But using "solar distances", and doing a "solar", is in principle the same as a lunar.  The Sun's orbit is simpler to model accurately, too---no lunar ephemeris nightmare.  But since the accuracy is so poor, you don't want to use the Sun unless you have no lunar ephemeris.

Planets like Venus or Mars could occasionally be a little better than the Sun if they make a close approach.

Cheers,

Peter