Using the Heads Off app seems to keep the screen from lighting up, but then the notification is not on the lockscreen or taskbar. I have to unlock my phone to see what the notification is via the taskbar, which seems counter intuitive. I still want my notifications of my lockscreen and taskbar, but I do not want my screen to light up. Didn't have that issue with HTC.
It must have something to do with the carrier, but who knows. I've seen other threads of people complaining about the same thing with this device on other carriers and there seems to be no solution. None of my apps are set to priority.