Interesting.
My logic goes something like....
A speaker will distort at a given spl regardless of any upstream settings. So any reduction in sensitivity on the processor will be balanced my an increase in overall volume setting - so the speaker is not a variable. And I thought that by reducing the sensitivity in the procesor there is a risk of digital distortion due to lower dynamic range at the processor. You have made me think again bringing in the speaker size which will make the speaker a variable.
I am not familiar with your speakers or amps. Could you be overloading the inputs to the amps?