You're making a good case for the use of supertweeters crossed at 10-12kHz. Halfway decent 25mm domes have wide dispersion to at least 10kHz.
In case You designed such a cross-over yourself, You might have seen the problem with the vertical nulls. Of course again, if the listener is forced to stay in between +/-5° or so, that might be accepted.
If not, what about something else addressing the drooping off-axis response? It is urban legend, that signal constituents above 10kHz contribute significant less to the musical presentation than anything else.
see >
ISO226:2003, musical content regularly has 10..20dB lower level above 10kHz than on average, added 20dB of less sensitivity of the ear in that range gives an attenuation of about 30..40dB, and then masking attenuates it further ...
But still there is need for the 'air' it brings. The supersonic parts above 10kHz could be radiated into the room using a single super-tweeter (for stereo), which is not aimed at the listener(s), but directed so, that it maximises the comb filter with all reflections. Such would enhance the spectral content, while not bothering the audience with inconsistent cues--due to irregularly correlated interferrence in the x/o-region.
Strange, a super-tweeter used very much like a sub-woofer? But bear with me. If the tweeter is not aimed at the listener, and its directivity isn't well shaped, the super-high hiss would to some part pass the listener anyway, only to come back from the walls, irregular, de-correlated, ironically very often from the backwall, from behind the listener. Listener should, as owner of platinum ears easily detect, that the sidewalls are dead quiet regarding that frequency range. The single super-tweet solves that problem.
Test it--we are DIY here. Run a super-tweet x/o'ed at the frequencies You suggested with some music. Aim it at You, aim it somewhere else ... report.
Thank You