The Sturmey hub wouldn't get "normal" gear on its test ride, so I had another go at the RH cone adjustment. It seems fine now, with nice wide sweet spots for each gear, at least in the truing stand.
If the RH cone is a bit too far along the axle, it can interfere with the action of the dog clutch. It has to be screwed in then backed off by half a turn and locked there (the bearings are then adjusted at the LH cone).
These new hubs are really very simple inside - planet cage assembly, gear ring, axle with sun gear, clutch key (which is what the indicator spindle/chain screws into), clutch and driver. An old AW had a more complicated clutch assembly, and the pawl springs were apparently a PITA to fit - the new ones are simple.