Yea... you have something wrong. Screen is low, when thats the biggest drain on the s3. If screen is low, the phone should be sleeping a lot, so cell standby should be top as it drains more than the system when asleep.
This suggests you have a wakelock which keeps your phone awake when the screen is off, keeping your phone running at full speed draining massive amounts of battery life.
FYI: The phone comes with a 2100 mah battery. So 4000 is a little less than double. At your current drain that would be right about 18 hours. Also, 2100 at the size of the stock battery is probably the current max commercial density. So, if you do want a bigger battery, it will definitely make your phone bulkier.
I also recommend avoiding Seidio up there. They have been shown to be over stating their capacity, and charge way more than other companies. 5 times as much in fact.
Finally, it would also help a lot when you post your screen on time pic, with latest main page of course, to also select the graph.... this opens a new window that includes a bar at the bottom showing time awake. If the screen shows off most of the time, but awake almost all the time... you have a wakelock. which is good news as thats very fixable. you could probably get double the battery life by fixing that.