Based on the measurements and the comments in
this review of the Epos M12.2, which I am assuming is not particularly different than the M12 in relevant respects, the comments by Duke (Audiokinesis) about listening height appear to be right on the mark. As well as the comments by Sideways about tubes.
The M12.2 has a considerable frequency response peak centered just below 1kHz, and another one around 4kHz, which the review indicates can be mitigated by listening from a point a few inches below tweeter level. That listening height apparently helps to smooth the upper treble response as well.
Furthermore, the impedance vs. frequency characteristic of the speaker is, in the upper mid-range and lower treble, close to being the exact inverse of the frequency response plot. Meaning that with a typical solid state amplifier having near zero output impedance, more power will be drawn at exactly the parts of the spectrum where the response peaks occur, presumably either causing them or further reinforcing them.
So first try various listening heights. If that does not satisfactorily resolve the problem, consider changing to a tube amp having relatively high output impedance (= low damping factor), although not too high or you will degrade bass performance.
Regards,
-- Al