Thanks for your ideas guys. I'll change some things to the list after reading your interresting points and add others.
Your ideas are safe in your answers but I think that some things are set in stone even if I'd like something else : theme park feeling, dialogs at camp, no more origin characters... I really think we'll have to deal with it.
Not sure about a "custom" cover mechanic
Hmm, I'll rephrase as my intention was not to get rid of it but that I want it fixed:
Because I can absolutely deal with it - but I want it to be ACTUALLY working. Refering mostly to Gale and his almost impossible weave-scene. Encouraging people to spam long rest in order to not miss out on companion dialogues has to go - there must be some way to make it work like in other games using similar mechanics (such as DA:O) where you can simply click on a character over and over until they are "done" and everything just goes in the order it "arrived" in.
It might not be ideal, and just like in DA:O I am expecting a whole bunch of awkward problems along the road with odd conversation-overlaps (like SH screaming at you, only to praise you 2 seconds later) - but it is much better than missing out on the entire conversation.

Other than just "please fix", I have a few other suggestions on the subject:
1) Let our companions TELL us when they want to say something. "Hey, I need to talk to you when we get to camp later" or a tiny chat bubble icon on their portraits. Or both - just let the player know WHEN companions want a word so we don't have to spam rest "just in case".
2) Somehow manage the overlap system so that we can have more than one conversation during camp. I get that some dialogues are conflicting (intentionally from a RP perspective, like who you go to with certain problems first etc)