Even when I don't slouch and try to sit straight up, I still get neck and back pain and cannot play for more than 15 minutes or so at a time. I usually play with the guitar going over my right knee. Is my posture wrong? This used to happen to me when I first started playing piano too. But the more I played, the longer I could sit without back pain.
You're probably tensing up without knowing it. Most sitting positions involving the guitar on the right knee have this. Try the classical position.
play standing up.