Are you OK with a 6 inch phone (phablet)? If you do I would suggest a Lumia 1320 mainly because it's got a very big battery (3400mAh) that would meet your long battery life requirement.

The downside is that the L1320 is a bit of an old phone, so you may have to wait to get future updates (Lumia 735 comes with the latest WP 8.1) and it doesn't have extra features (no SensorCore).

If not, then a Lumia 735 is not a bad choice. I can certainly last a full day with my L925 which has a 2000mAh battery and I bet the L735 could too.

Others have suggest a L830, which in my opinion doesn't really offer more than the L735 other than a better camera.

On a second thought, the L735 might not be great for you since it doesn't have glance feature. So if you go with the L735, you might have to unlock your phone every time to check your social updates.