OK, I lied when I said the hip pain wasn't as bad now that I've been using the pillow. It really depends on the night, apparently. Some nights I can sleep just fine, and wake up with no problems. Other nights (like last night), my lower hip (the one I'm sleeping on) gets pretty painful, and rolling towards my back or towards my belly doesn't alleviate it.
I read in a forum somewhere that it might be relaxin loosening up my hips, and that putting the pressure of the rest of my body on one hip is slipping it out of alignment. That makes sense; usually when I turn over the formerly painful hip feels much better, and soon the new lower hip is hurting. And then my lower back gets sore, which could be a lack of alignment (hips getting wider, making my spine curve) or it could be the muscles there trying to help my hips. Dunno. What I do know is that it's time to start doing more gentle yoga at home.