I think you could have had her really screw up during the Mabrae section of the mission and have Picard threatening to kick her off the ship, only for her to then make the solution that she eventually comes up with which convinces him otherwise but then, in the aftermath, I'd have shown more clearly that she's making a concerted effort to fit in with the crew, biting her tongue more often.
Again, it wouldn't have been possible to kick her off the ship at that point, because a) there were no Federation facilities anywhere within range and b) they needed her on the mission. Given that she was there for the express purpose of helping with the mission to the star cluster, it would've made no sense whatsoever to create some artificial jeopardy about whether she'd make it that far.
(And by the way, one person can't make a concerted effort, unless that person has multiple personalities.)
And I've read elsewhere at how some people have said the characters very much a Mary Sue (the same allegations people have said about Grimm Vargo in Before Dishonor) - and, at times, this does seem like it could be borderline true.
The term "Mary Sue" tends to be defined so broadly and inconsistently that it's become fairly useless as a term of criticism -- indeed, if the term is being applied to a character as far from the original definition as Grim Vargo, then it could potentially be applied to anyone. People seem to use it simply to mean "a character I don't like."
Strictly speaking, a Mary Sue is an impossibly idealized character who outperforms all the other characters and earns their undying devotion. None of that applies to Trys. She's a very flawed character who has a lot to learn from the other regulars and gets on their nerves a lot. If any new character in GTTS is idealized, hypercompetent, and highly popular with her crewmates, it's Jasminder Choudhury.
True, one aspect of a Mary Sue is that the author has a special affinity for the character (who's usually an author surrogate) and plays her up a great deal because of it. I'll admit, I'm very fond of Trys, and she does have a few author-surrogate qualities. But I did try to balance her with the other characters rather than making her too dominant. And I grew pretty fond of Choudhury too.