I don’t know if Stephen Lansing is aware of that particular institution but I’d certainly never heard of it. Though there are numerous examples of resource management institutions/systems, many water-related, dating back centuries, and in many parts of the world. And on the face of it, many seem to be good candidates for demonstrating emergent properties. The Dutch water boards mentioned in this (and a previous) DI article are another example. Such systems have been studied by numerous other researchers over the years – including of course the late Elinor Ostrom, the economist/political scientist who won a Nobel prize in 2009 for her research into common-pool resource management systems – aka ‘the Commons’.

As you suggest, it seems demonstrating the emergence – the complexity – is the hard bit: identifying the key parameters and functional relationships, mathematising them, and showing the resulting model outputs to be consistent with real world observations.

On the subject of stuff I omitted in the interests of avoiding article-bloat, the UN Food and Agriculture Organization website has a great list of ‘heritage agricultural systems’, many of which seem similarly good candidates. And in Asia, they often seem to involve irrigated, terraced rice fields. See the Dong Rice Fish Duck system for example:
https://www.fao.org/giahs/giahsaroundtheworld/designated-sites/asia-and-the-pacific/dongs-rice-fish-duck-system/en/