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Greg,

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This result lead me to wonder how navigators or map makers (thinking of Thomson or Powell here) would have taken these shots if they were by themselves and did not have assistants simultaneously shooting the altitude of the star/sun and the moon?

You can find details of what Major Wesley Powell did in his 1869 expedition in section 4.8 of the paper available here https://www.cambridge.org/core/journals/journal-of-navigation/article/astronomical-observations-of-the-1869-powell-expedition-through-the-grand-canyon/D5627421BA12E49147E637BAE25F497F/share/d3684665dccf0a25c69599b9f08bc483f2be78a2

A general overview of the techniques he employed can be found here http://fer3.com/arc/m2.aspx/Astronomical-Observations-1869-Expedition-through-Grand-Stuart-sep-2020-g48707

Recommended standard practice was to measure the altitude of the star and Moon, then take multiple measurements of the lunar distance over a 10 minute period or less, then finish with a measurement of the altitudes of the Moon and the star. Averages are used in the reduction. Powell had not planned to use lunars and some of his rounds of sights lasted over an hour. While this is not fatal, it does make the reduction non-standard and considerably more complicated. We found that none of Powell's lunar distance sights gave plausible longitudes,

Robin Stuart