But that's exactly what I meant with the mathematical function converting between a HATS and free field measurement. If you know one, you can calculate the other. Again, minus tiny variations which as far as I'm aware do not matter; why do you think this set of acoustic filters changes with a different speaker, enough such that it would invalidate what we get from a free microphone? Note I'm genuinely interested, because what I'm writing here is what I was taught by people running experiments with HATS. They could be wrong or overly simplifying, but they seemed qualified enough.
Yes HATS is designed to test binaural effects, but that's usually for things like stero, sources at different angles, and so on. For reproducible speaker measurements the source would always remain at the same position, right in front of the manikin, right? Also meaning both its microphones will measure the exact same signal (unless room or manikin itself aren't symmetrical but that's not useful), so there's nothing of binaural interest going on.
edit don't have a lot of time now but: this figure from
https://headphones.com/blogs/features/diffuse-field sort of seems to explain what I mean; the top-right is the frequency reponse of the HATS which comes as a calibration file with the device, for various elevation/degrees. Unless I'm missing something it tells you the fixed relationship between measuring with a freestanding microphone, and what you'd measure at the HATS' eardrum. And the 'perceptual' is also what you get when measuring the genelec with a freestanding microphone roughly at the head position, no?
And, quote from the same page: