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Agree the key element is a distant event that half the Earth can observe in unison.  If a good way is available to get local times of that event, then I also agree that parallax plays no part.  It is only because I'm trying to skip determination of local time and use angular RH offsets from local meridians as the path to longitude that the parallax comes up as large enough to require at least a coarse adjustment.  I could still be thinking about it wrong.  

--Lyle Ruppert