I made a test with my voice today. It was ok…
I listened again to the fragment under question. Incredibly, it might have to do with the singer’s way of singing itself.
I say incredibly, because the waveform is not even halfway to hit the ceiling, volume level is safe below the red zone, yet the result sounds jumpy (in the sense that it makes you jump in your seat from the effect it has, sonic, emotional or whatever…)
Tommorow I have a session with a different singer. Hopefully everything will go smoothly.
Thank you all for the feedback!