Honestly, it's not so much about the romance as it is about my how my character's animations would look in those scenes. I am expecting a lot of laughter from the awkward animations.
Edit: And yeah, L from deathnote.
I love L!
L as Inquisitor... he would have found Solas out long before Trespasser!
Dammit, I'm out of "likes", AGAIN! 
That's the only non spoiler thing I can say about that chapter!
Well, at least you like it!! (that's something x-x)
Honestly, any comments would help. Even just what you would wanna do if you fell into Ancient Elvhenan, and what you would most like to read.
Knowing that you didn't completely cringe like "oh god what a horrible idea ew" makes me happy though. I'm verrryyy self-conscious about my writing and ideas. It causes me horrible anxiety. 
It's okay Crusher! You seem to have some great ideas, you just need some thought to refine them.
To keep yourself from Mary Sueing I suggest you think of some realistic flaws for your main character. Perhaps things that would contrast to Thedas but are prevalent in our society. Maybe she's a coward, or a germaphobe, or super out of shape and lazy, or she's squeamish, or she complains a lot about lack of comfort (like from not being used to Thedas clothing and beds and food).
Also a lot of fanfictions have problems with their original characters because they make them too well liked by other characters, or they too often make them the key to solving all the worlds problems. I recommend this article by TV tropes for help with your original character.
Do you plan for the long dead Lavellan to have been in a romance with Solas? And do plan for your new character to romance him? That can be very tough to write. Even with her dead readers might be resentful of your OC and Solas getting together and Solas moving on from his vhenan. It could be easier to have him never have had a vhenan in the first place. But that all rests on you and how confident you feel about writing what could be a very complex romance and situation for your characters.
Also, did your character play DA? Does she like Solas's character (it might be an interesting twist that she didn't like his character)? Is she upset about what he did? Does she think she's hallucinating or dreaming and does that make her reckless in the beginning? Does she miss her old life or is this the adventure she was waiting for? How does she explain her presence and the things she knows?
I like the idea of a modern girl saying she was an observer from another world. Explaining it like a spirit looking through the Fade, but she instead was a person looking through at another world. She's not lying per se, but she's not telling the truth either. And how could you tell the truth?
What's interesting about the modern girl connection with Solas is that she very possibly would be in denial about the realness of these fictional characters. Very similar to the way Solas saw the world, perhaps she even needs him the way he needed her to see the world as real.