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Stanford definitely has one of the better programs in Econ history. While you are correct that Amemiya is essentially retired, Gavin Wright is one of the biggest names in Econ history, although he does mostly US economic history (although he'll likely be retiring in the not-too-distant future).
Off the top of my head, I can't think of any economic historians who are economists in the US who does much in that area. Maybe some in the UK or continental Europe? My impression is that the most active ancient societies for economic historians to study are Chinese and Muslim, since there are plenty of records that have not yet been translated and analyzed by Western trained economists.
While there are faculty in other disciplines (History, Classics, Archaeology, etc) who focus on it, within Economics Departments I think that you'll find it to be a virtually non-existent job market and I would heavily discourage anyone from doing a PhD Economics in order to study economic history. Amemiya established himself as a theoretical econometrician and only ventured into Greek economics history because it provided a novel way to tackle issues that interested him involving applications of cliometric techniques that he pioneered. To be perfectly candid, unless you have a cache of previously undiscovered material to investigate, I cannot imagine that it will be the most fruitful area for an economist to study.