Well I'm sorry to disappoint you Butcher, but there isn't any proof, and there isn't likely to be any more proof or evidence forthcoming as the years go by. Quite the opposite I should say. The production records were mostly destroyed and the aircraft lay broken and scattered all over the Pacific theatre, along with a lot of the personnel involved. We have to use deduction and reasonable assumption and extrapolation.
To whom do you need to prove it to and how much convincing do they need? The Imperial Army hardly commissioned Nakajima to make this up-armed version while they were still making the Ko only to have them do what? Serve as trainers? There are photographs of Otsu fielded next to Ko, in Sentai markings. And there aren't that many photographs of the Hayate in the first place compared to say the Spitfire.
The Otsu is nothing special, no experimental equipment, no remarkable engine or special features, just a slight armament upgrade and a tiny bit more power and less weight over the Aces High version of the Hayate and that's only because it was based on the Late Production Ko.
Does it qualify? I don't know because I have still heard no confirmation of HTC's conditions. I have pointed out twice previously that there is the opportunity to economically include three non-experimental production models of the Nakajima Hayate if the 3D model is ever revised. Whether there is the will to do so is another matter.