Great write-up, Nagasaki Joe! We are set to stay at Ryotei Hanzuiryo this coming December, and booked one of the two Tokubetsu Shitsu (special room) there. Like you, it's taken a while for us to finally pay this ryokan a visit, for some inexplicable reason.
When I spoke to the manager over the phone, he mentioned that the outdoor open-air bath in our room is real Onsen. Is this only the case with the Tokubetsu Shitsu, or perhaps he was incorrect in his explanation?