I'd offer a different suggestion: Replace the receptacle with a back WIRED one, rather than back STABBED. The kind with rear-entry screw-clamped terminals. They can accept all eight wires and are much more secure. Pigtailing that many wires in a normal box will be pretty difficult and in my opinion it doesn't add any more reliability over using a backwire receptacle.
Just so I am clear, does back stabbed mean the holes in the back that you just jam the wire into? And these are not recommended but the rear-entry screw-clamped terminals are fine?