The XPA amps are rated for 4 ohms loads, so 6 would be no problem. My question is, what volume is your AVR set at when you notice the sound issue? A room that is 15 x 15 would have limitations that might be affecting things, depending on how loud you are running at.
I looked it up and your Pioneer is THX Ultra rated. That speaks to higher class amplification and I'm familiar with this because my Onkyo has the same rating, and it doesn't run out of steam as easily as a mid level avr. The reviewer was pretty impressed with the Pioneer room correction, that was my next possible issue. Were you satisfied that the set up ran correctly and the results were good?
Other than that, it is possible that you are running out of steam and a separate amp can certainly help there. I actually added an Outlaw 125 watts x 7 to my Onkyo, which has the same wattage output as your SC 57 and the improvement was noticeable, though my issues weren't volume related. I'd think though that the XPA-5 would be a good place to make an improvement if my above suggestions aren't a cause of your issues.