The problem is that EHG needs WHG and CHG needs EHG. So here i dont know what i'm talking about, but exactly how could WHG be in East Caspian? The EHG needed in CHG cannot be ANE itself, because it's already in Iran_Neo. Also, remember ourselves that Dzudzuana is not directly related with CHG, but is highly related with Anatolian and Levante Neolithic. It looks like the ancestor of CHG, but not CHG proper have to come from Eastern Europe and get BA ancestry South of the Caucasus at some point. We are probably talking here about something that old as Epigravettian in North Caucasus.
Most of this will probably be answered when the source of the East Eurasian ancestry seeping into West Eurasia in the timeframe between Dzudzuana and Huto/Karelia (as well as speculatively Villabrunna) is discovered.