I'm only listening through laptop speakers (with a toddler running around the room) so can't really hear the distortion. But:
I know the M10's mic input can take a fairly hot signal but that's the first thing I'd change - I always go line-in unless it's a desperately quiet show and I need some extra gain. Having said that, I'm not sure I've ever done that with the M10.
And is your battery box's battery fresh?
The fact that you had to set the M10's gain so low (I usually need go no lower than 5/6 - often higher) suggest to me that you were overloading either the mic input or the mics themselves. As per similar threads here and elsewhere, I suspect you may need to run modded mics or use a 3-wire box. I do the latter when using At853s and have never once had an issue even at very loud shows.