Wow, you gonna get sunburn from that amoled display of your GN2! Seriously, you are the minority, an average user needs to attend actual face to face meetings, work on a PC, answer the poor old analogue phone, play with own children, concentrate on driving, etc, rather than spending hours watching movies on a smartphone each day.
Since getting the N4, my interest in the latest and greatest have waned, and I no longer feel the urge to upgrade… at least till the Nexus 5 comes along. I live in a country that is yet to embrace LTE and I don’t need removable storage or battery.
I think best get a replacement, I have the second batch of Nexus 4 which is considered early, yet I have better screen time. I know battery depletion can be quite alarming sometimes on menial tasks but not as severe as you described. Good luck!