By the way (jeez I post a lot, like A LOT)..
I thought about it some more (I probably slept on it since I woke up with these things in my head) and I've come to some ideas.
There is the fact that the Inqi's mark is permanent, while it could be so that the player can close rifts after end game it feels a bit off - they had no issues removing other things after the end of the game -ahemsolasahem ahemconversationsahem ahemmyromancedblackwalldisappearedfromskyholdalthoughstillinpartyaheem-, and since the breach is finally closed it'd be more likely these rifts will close (I closed all of the rifts before the game's end, but I suppose they stay open, right?).
So, me thinks it's a plot device within all of that Solas mystery solving arc that should be. I'm not sure what kind of relations the anchor has to Solas after the ritual but it is a key, to open things and to close them. Don't you wonder if that applies for things other than the fade?
Besides that, there is the Well of Sorrows. If your Inqi drank from it they are bound to Mythal and to Solas in return, if Morrigan drank from it she is bound. That connection could play a part in how they discover Solas. Also, since Inqi/Morrigan own the knowledge of the Well of Sorrows they might be able to find more about Solas in general. More than anyone could find out in the current era. Inqi/Morrigan is sort of a connecting bridge to Solas' past.
And besides all that, all that friggin' talk of 'spoilers!!' whenever Weeks is asked something about Solas is... Intriguing. He could be trolling but if he does he will invoke the super-special-awesome rage of lots and lots and fangirls and fanboys.
This all brings me to think that
THERE MUST BE A DLC, or a game with Inqi as main (less probable of course).
Inqi is probably the best way to bridge this, and seems that after Mythal got.. eaten or whatever... that Inqi's the only one who could actually move the plot around him.
Even if Inqi hasn't romanced Solas.
Seriously, I spend so much time reassuring myself that it isn't over, so I could pick up my Lavellan's playthrough after that 3rd romance scene and continue playing.