but how does one "decide" to operate at a specific level of distrotion?
You don't it is a function of what signal you put into it. You put in a signal that has a 1% total harmonic distortion then that is the power curve you get. If you put in one with 10% then you get the other curve. If you put in a signal with 20% THD then they are not saying what power you will get.
Just because a speaker is running at less than its rated power does not mean it will not distort. The same goes for amplifiers.
To find out the cause of the distortion look at the signal with an oscilloscope, if the signal is not distorted but the sound is then it is your speaker.
Remember those circuits in the data sheets are just starting points for a practical design not a finished design. Supply decoupling is important as well as filtering and correct capacitor type selection.