A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: David C
Date: 2017 Jan 6, 18:02 -0800
What you have described is the core idea of moon culminations, an old method to determine longitudes of fixed points. The largest error came from the Moon ephemeris, so transits were also observed from a point of known longitude. That cancelled the ephemeris error, and you ended up with the longitude difference between the observatories. Lunar culminations generally had lower accuracy than the mechanical solution of transporting sets of chronometers back and forth between the observatories.
This 1870 report about determining the longitude of Wellington covers all of your points. Lunar culminations, using the moon ephemeris as an interim solution, observations at a point of known longitude (Greenwhich), transporting chronometers, and the electric telegraph (within NZ). Lunar culminations were considered inferior to transporting chronometers. There is no mention of Lunars.