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This method is essentially based on the Moon parallax.
(Imagine that the Earth is very small. Then the
method will not work: all lunar distances are
the same, independently of your place on a small Earth).

To estimate the accuracy, notice that the ratio
of the distance to the Moon to the Earth radius is
60 (very roughly). So the loss of precision due to the
method is by the factor of 60 under the most
favorable conditions.
These most favorable conditions are:
a) The Moon is near zenith, and
b) The two directions Moon-star are perpendicular.

So under these conditions, the method is less accurate
than the usual Lunar distances by a factor of 2.
If the Moon's altitude is 30,
multiply by enother factor of 2.

Now it is hard for me to believe that one can
measure distances with 0.1 or even 0.2 accuracy
permanently and reliably:-)
Some results posted by Frank seem to show that he can,
but it is still unclear whether he posts his best
results of average results:-)

I still have no definite opinion on this matter,
but my analysis of observations of Cook's expedition
seems to indicate much lower accuracy than 0.2'
And this was done from the ground,
by professional astronomers, possibly with the best
sextants ever made (?)

The Lunar method was advertized as having approx 1/4 of
a degree accuracy. This I believe.
Then the lunar-with-chronometer-but-no-horizon
method has probably 1/2 degree accuracy or so.

Alex.


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