What I want is a new character that is somehow related to the quissy's mission to stop solas (i.e. works for them, starts an organization parallel to them, etc.) I want the inquisitor to be heavily involved, I just don't want to play as them. I think it could be done, as long as the inquisitor is tied heavily into the story.
yeah and I love that 
The only way to have Quizzy heavily tied to the story is to have them either as significant NPCs or secondary protagonists. Mission boards or letters just don't cut it, and I see way many more problems with making Quizzy an NPC.
In many ways Hawke as NPC was simpler - yet it still didn't please many people.
And not only their story was smaller, their involvement with DAI's antagonist was smaller as well (they've only had one type of relationship with them - that of an unfinished business), they've had the benefit of three distinct flavors of personalities to choose from in DAII - dialogue options given to Inky weren't as pronounced, but allowed for far more nuance between them. So... how can they even try and implement that without ruining Inky for most people
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IMO the interesting option would be taking control over Inky at some crucial point in plot - they may have a limited options in dialogue, but enough to give people enough of a flavor to them and re-establish their personality and goals. Then the game may read Keep choices and crucial choices made throughout DA4 and associate them to one or two (or three or four??) NPC responses they could have, be it while interacting with DA4 protagonist or Solas.
Same with DA4 protag in case they'd be temporarily made NPC - if enough crucial, personality-establishing choices would be made, they could act 'on their own' when we switched protagonists.