I found a solution to the volume problem, or at least - an explanation.
A lot of people are using the free in-ear headset provided with the PS4. That thing has a terribly quiet microphone - no matter what headset you buy, people using those are going to sound quiet.
I tested this theory by purchasing 2 P4C's, and sent one to a friend. As soon as she unplugged the 'free' headset and connected the P4C, the volume was perfect.