turn off LTE if you are not using it.
download better battery stats and CPU syp (just until you figure out whats going on)
open BBS, and see if you have any partial wakelocks
if you do, this is probably keeping you awake running the CPU at a low frequency instead of deep sleeping.
open up CPU spy and see what percentage of Deep sleep you are getting. it should be the majority of the time...if it is not, you have something keeping the phone awake.
FWIW, 2 hours screen on is not terrible battery life. i would expect more, but its not horrible. maybe 2.5 hours.
i can go 18 hours on a single charge but my screen on time will be right around 2 hours....or i can go 6 hours like you but it will also have 2 hours screen on time. overall time doesn't make a huge difference, it is screen on time that you have to watch out for...and i would say you are just below average.