Okay, so you have two separate amplifiers behaving badly at the same time. Is it possible that both amplifiers have problematic issues with wiring or speakers after the amplifier? Maybe. But what do they have in common? The source electronics and the voltage.
First, substitute another source like an ipod direct....although the ipod may not have enough output voltage to trigger the problem....so try the ipod headphone out jack. Or try another substitiute CD player, any other player.
Next, and most important, measure the voltage across the amplifier primary terminals when the problem occurs, withOUT the boat running, and NOT at the battery terminals.
Something should be revealed.
This is the time of year when worn out batteries begin to surface as well as bad connections/terminations from a summer of shock and vibration.
Don't forget about exposure to water. A wet source unit could behave this way.