Let me refer to this article that is best viewed alongside the other TV Tropes link above:
http://tvtropes.org/pmwiki/pmwiki.php/Main/CommonMarySueTraits
Here's what features I see in that rundown that seem to be exhibited in the fictional Lady T'Anna:
"Highly persuasive, regardless of the actual content of their conversations."
There are some elements of this, although much can be forgiven as the character is an ambassador.
Which I most emphatically am not. I am not good at living out of suitcases, shutting myself in conference rooms for days on end, or soothing overlarge egos.
"Is either brave and cheerful (despite her past"
This, in small part. She's very well put together for someone who's been through everything she's been through.
Guilty as charged.
"A perfect singing voice. Most often shows up in Mary Sue Classic."
Ayup. That said, Spock receives the following quality also common to Mary Sues: "Extreme proficiency with an instrument of her choice."
That goes back to the first season of TOS. We learn in "Charlie X" that Spock plays the Vulcan harp, and as you note (if you can forgive that pun), we discover in the third season that Spock can sightread on a Terran piano. I wanted to give him and T'Anna an obvious commonality, and music seemed to me to be the (forgive me again!) logical choice.
"Just random magical powers, such as telepathy in a universe where it's never even been mentioned."
Are we to imply from the story that T'Anna is more than a Flint who simply moves from place to place, but a being who has lived several finite lifetimes?
Yes, that was what I was after.
The parallels are not unwelcome, though, especially since that's one of those wild Ancient Aliens-esque characters from Trek that I really dig! I like what's done here, especially the tie to Saavik, but it's a quality that's on the list nonetheless.
No Physical Appearance or
Accessories tropes that I could identify. Maybe the "spritzer", but somebody had to explain where soft drinks went in the 23rd century. 
Down the hatch, just like they do now.
"Some Wish Fulfillment with a character you think is hot isn't that bad. But Mary Sue seems to grab their attention straight away. Even if they already have a stable love interest in canon"
You split the difference here. Tying T'Anna into Saavik in such a way is something I liked, as I mentioned. But pretty much off the bat, Spock is into this lady. The use of pon farr as a device disguises it but it's still there.
"She's dating the author's favorite character"
Just guessing here, but if so, eh, it's a related trope. Haven't we all been there at least once, though?
More than. Definitely more than.
"Mary Sue is always on the Spotlight-Stealing Squad. Without her, there would not be a story."
Laughing! May I borrow that, please? That's excellent!
Still, it's bound to happen.
As I said, you're being charitable.
"Perform a Heroic Sacrifice as a way to prove that she's Too Good for This Sinful Earth."
Okay, so no sacrifice here but still, the MARY SUE DIES trope is in full force.
I would actually argue that there is a sacrifice. T'Anna knows that the drug poses the very gravest risk to her health, but she takes the risk anyway because she knows that hundreds of lives hang in the balance.
"She might turn out to secretly be half-human, half-(insert species here)."
There's precedent in canon. No worries, and this is more like 1/16th Klingon in her case?
Forgive the correction, but T'Anna is one-fourth Vulcan and three-fourths human. It's her human uncle who marries a Klingon. Although now you have me wondering how a human-Vulcan-Klingon hybrid would act . . .
"She will often have a tragic family life. Coming from an abusive background is quite common."
Yup. This is also fairly well-telegraphed early on in the story; not sure if you were going for that but be mindful if not.
Thank you for the heads-up. I was definitely going for that, although the beans don't get spilled until the first Sickbay meld.
"May be named after the author in some form."
Yeah, you went there. Would be curious to know if a simple name change would help the reaction to the story. Just make sure you don't pick one of these!
T'Anna isn't my given name. I've chosen variants of it to be as consistent as I can across multiple forums/fansites (some of them play nicely with apostrophes in usernames, while others don't). Having known this character as T'Anna for more than two years now, I just can't see changing her name. (The name "T'Anna" was claimed on another forum, so I had to think of an alternative. Adding "Lady" made sense because in TAS, Spock's mother, as the wife of an ambassador, is referred to as "Lady Amanda.")
*does the same*
Thank you so very much for being so patient and so thorough in your responses. I was inclined to go down the list in order to address it point by point, only to discover that you'd beaten me to it without benefit of meld.
