My group is considering a houserule whereby you would not be eligible for Righteous Fury on any hit which already deals multiple dice of damage due to scatter or auto-fire. So yes, you'd still get it for tearing weapons, grenades, high damage weapons etc, but not if you get hits with scatter or auto-fire.

Does this sound like it would really have any significant impact upon the flow of combat? I mean, if you are rolling 7d10 for damage because you got a boat load of successes with your bursting combat shotgun, does one re-rolled die really matter?

Well it does make a difference since you deduct armour and toughness fron each hit.
So it is not 7d10+28 but 7x 1d10+4 incase of the shotgun.

Santiago nailed it. Burst and Full Auto hits are always treated as seperate hits, meaning that if your enemy has good enough Armour and Toughness Bonus, he won't give a **** about your 6*(1d10 + 2 - 11) damage, making Righteous Fury quite important.

Good points... So far we're mowing through the opposition (and getting mowed down ourselves) with scatter / autofire - though its more the autofire than the scatter. Granted, we're stuck in void suits at the moment, so only 3 points of armor.

Thanks for the feedback.