I would like to offer yet a couple of other pieces of evidence of the first type (an abbreviation explained) and then consider the question of when and how the other interpretation - sefardi tahor - came from. Previously I'd shown how in the 19th century Jews with a living tradition of its use did not understood it to mean sefardi tahor. Here is a page from a 1780 book on rabbinic abbreviations by Gottfried Selig called Compendia Vocum Hebraico-rabbinicarum:
Here's another, from an anonymous manuscript called at the beginning ספר ראשי תיבות, described as (Italian, 18th century).
By the way, many people do not realize that even though shlita is used today as something one writes about others (i.e., a notable rabbi) it really is only a good wish and people used to use it, or a version of it, for themselves. The abbreviation שליט"א stands for שיחיה לימים טובים אמן, and is sometime shortened to שלי"ט, particularly when adding it to one's own name, which would then mean שיחיה לימים טובים. Yes, this is the origin of the Jewish surname "Shalit." Since "שליטא" is also an Aramaic/ Hebrew word referring to rule and authority, I assume that's why this good-wish abbreviation came to be used for notable rabbis (notable rebbetzins get the grammatically appropriate "תליט"א"), and also why it's really not seen as so appropriate to use for oneself.
Nevertheless it is undeniable that we find many people adding שלי"ט to their own names. Furthermore, I once posted the following penmanship doodle in the blank pages of the famous Munich Talmud manuscript:
As you can see, young (?) Uri Yehuda added שליטא after his name, and I don't think he was being arrogant.
Getting back to ס"ט, "sefardi tahor," it is interesting that there is at least one 18th century source discussing it from that point of view. It is in a manuscript by a very prominent 18th century rabbi, R. Pinchas Katzenellenbogen (1690-1760) called יש מנחילין, which wasn't published until 1986 (link). In it, the rabbi recalls his own father R. Moshe (1670-1743; who was rabbi of Fuerth) explaining to him why Chacham Zvi signed his name ס"ט despite being Ashkenazi, and despite the abbreviation meaning sefardi tahor, or Sefardim descended from pure and holy ancestors who never converted.
He recounts a version of the well-known story about how Chacham Zvi's father was almost killed by marauding Cossacks, who spared him out of mercy (yes, that's right). They did not spare many others and he survived for days pretending to be among the dead and scavenging for food at night. In the meantime, his family did not know what had happened to him and his wife was an agunah until witnesses came and claimed to know that he had been killed. She was permitted to remarry - but then her husband returned, very much alive.
The version here takes place in Ofen in 1686, during a period of war between the Ottomans and Austrians. Chacham Zvi's father was captured by the Austrians, but the rumor was that he had been killed. His father-in-law was able to gather testimonies that he had been killed, and he therefore permitted his daughter to remarry, and soon she was engaged. In the meantime, Chacham Zvi's father escaped or was redeemed from his captors, and wandered where he could. He happened to arrive in the city in Bohemia where his wife's soon-to-be second husband lived! To make a long story short, he was able to make himself known and recognized, prevent the wedding and reunite with his wife. Because of this near-brush with impurity (i.e., a married woman marrying another) and the success in preventing it, his son Chacham Zvi would sign his name ס"ט in commemoration of the purity of his ancestry.
Of course this is problematic. Chacham Zvi was already 30 years old when all this occurred, in this version. In addition, the end of the story seems to have forgotten the beginning: R. Pinchas specifically defines it as standing for sefardi tahor, and the problem as being that Chacham Zvi was Ashkenazi. Very strange. Not only that, in the next chapter of the manuscript R. Pinchas (who we recall was born around 1690) adds a fascinating story about how one time in Brody he stayed at the home of R. Nathan, the Chacham Zvi's son. Not only that, two of R. Nathan's brothers (R. David and R. Ephraim) were there as well. And after the the Friday night meal, he asked them if they knew the reason why their father signed his name ס"ט? And they told him that they did not know the reason, for they were small when their father died. So he told them the story, which they had not known! And they said to him, if you had came here only to tell us this story it would have been worth it! (The story begins here and continues for 4 pages.)
Very strange. That said, it is conceivable that the point is that Chacham Zvi took it in a non-literal sense and only adopted an existing, well-known abbreviation referring to the purity of one's ancestry. Of course all the other evidence, that those who used it meant "sofo tov" or some variation cannot be ignored. Still, we have a unique piece of testimony from the 18th century that it means sefardi tahor, and this proves that, at least in Poland, people thought that it's what it means.
In all likelihood the simple explanation is that it did not stand for sefardi tahor and the reason Chacham Tzvi used such a Sefardi cultural affectation was because it was yet another of the several Sefardic influences upon him. First, he grew up in Ofen. Although this city was mostly Ashkenazic, there was a powerful Sefardic influence in this Ottoman-controlled city (Ofen is Buda in Hungary). Secondly, he was educated in the Sefardic yeshivos of Salonica. Third, his son R. Yaakov Emden writes that he possessed responsa manuscripts written by his father in his youth. He did not publish them, he says, in part because they were written in the Sefardic script and difficult for him to read - וגם הכתב היא ספרדית ובקושי אוכל לקרותן.
I thought it would be interesting to show the sefardi tahor version as it is nicely explained by Mendel Mohr in Hamaggid Year 7 #8 February 19, 1863, pg. 62.
As you can see, he actually accuses someone else of stealing his explanation that s"t means sefard[sic] tahor. I think it's worth pointing out that Mendel Mohr was from Lvov, and the fellow he accuses was in Zolkiew. These are both in Galicia. The story where R. Pinchas Katzenellenbogen tells Chacham Zvi's three sons what s"t means as used by their father? That occurred in Brody - in Galicia. The visiting sons of Chacham Zvi? They were from Lvov (Lemberg), same as Mendel Mohr more than 100 years later.