NavList:

I'm thinking of the "0" case:  Ptolemy sends his graduating scholars to far-flung locations to take up teaching.  He sends instructions of what to record every time they are able to observe a lunar eclipse properly (cloud free and adequate setup).  As the years go by they circle back to Alexandria and turn in their data for the five or six eclipses they have observed.  I may have a conceptual error somewhere, but I think the following would work. 

Setup instructions:  Find an observation site and place a conspicuous survey monument there for aftercomers to find. Note rough vector offsets to nearby cities, towns, mountains.  Carefully determine a north/south line and local latitude.  Set up a plumbed meridian plane topped with an axle sloped parallel to the Earth's axis and a swinging observation plate hinged to the axis (armillary-like, but less) .  Every eclipse, record the place, date, angular swing needed to bring the moon into the measuring plane, and whether the moon was ante or post meridian.  At the same time have someone measure the altitude of the moon above true horizontal.  No clock involved.  Bring all those observables for a few eclipses back to your alma mater.   

From any set of simultaneous observations Ptolemy can calculate a first iteration of relative longitudes and then use those, along with the latitudes and altitudes, to estimate a parallax correction (more accurate if he already has worked out an atmospheric refraction table) and iterate longitudes.  Any zero convention can then be applied, and the resulting prime meridian would not need to pass through any particular "observatory" (e.g., Alexandria could be declared 60 deg east).  (You could also derive parallax without the altitudes, given enough eclipses.)  

Note that if you really want the local time, you can just use the angle of the moon from the meridian.  Necessarily, the Sun is the same angle from the anti-meridian.  It doesn't seem necessary, though, to convert to time just to convert back to angles in making a world map.  

A single eclipse is visible to only half the world, but over years of observations longitudes could be established around the world.  The mother ship of Alexandria would not need to be included in a particular set of shared observations to make them valuable.  Note that the estimate of parallax does not require separate knowledge of Earth radius or Earth-Moon distance, but if you happened to have an independent estimate of Earth radius then a Moon distance estimate would follow.  

--Lyle Ruppert