You don't want to go with a lower speaker impedance. You want higher impendance.
32Ω or 600Ω would be nice.
Try putting a 33Ω resistor in series with your 8Ω speaker.
Edit: Try putting a 470Ω resistor in series with your 8Ω speaker. Add a 10μF capacitor across the speaker.
The reason the tone in the video sounds acceptable is because you are listening to high frequency tones. The harmonics are pushed out of the range of normal human hearing. At lower frequencies the harshness of the odd harmonics is more pronounced.
32Ω or 600Ω would be nice.
Try putting a 33Ω resistor in series with your 8Ω speaker.
Edit: Try putting a 470Ω resistor in series with your 8Ω speaker. Add a 10μF capacitor across the speaker.
The reason the tone in the video sounds acceptable is because you are listening to high frequency tones. The harmonics are pushed out of the range of normal human hearing. At lower frequencies the harshness of the odd harmonics is more pronounced.

