It's probably worth point out that we are getting XP for various bits of conversation.
The problem is that the display for the XP doesn't always come up due to still being in dialog when you get it. You can only tell you have it by either noticing you have leveled up or reading the combat log.
I did a zero kill dialog based warlock run and managed to get to level 3 before getting bored and triggering the end of the EA. (full disclosure, I did get some small bits of XP from combat where a neutral or friendly character killed an enemy before I could run away)
So between dialog and exploring, i think you can stay on target. They really need to improve the XP display though, it's very easy to not notice that you have gained XP
