Why does the Conservative Movement pronounce Hebrew in a quasi-Sephardic pronunciation, even though their engagement in Wissenschaft Des Judentums would have led them to embrace the Yemenite pronunciation?
Very simple. Due to the influence of Zionism and the state of Israel, where such pronunciation was adopted, the conservatives copied it at some point.
The "quasi-Sephardic pronunciation" you refer to is actually Israeli Hebrew which the Conservative movement (and Modern Orthodox movement and Reform movement) have lately been teaching.
The traditional Conservative movement was built off of the Reform movement which was built off of German minhag - thus a boy wears a tallis when he turns 13, regardless of marital status, and people spoke in the Hebrew of their parents. Even my parents, growing up in Conservative shuls in Brooklyn (1950s-60s), pronounce G-d's name with an "oy" not an "ai" and learned to soften their savs.
Here's an interesting piece on the rise to prominence of Israeli Hebrew in America - not limited to the Conservative movement. (Though it's simplified a bit for the audience, the links therein are good sources.) The main point apropos your question is that in America, it was easier to find Israeli Hebrew teachers, the movement is Zionist, and that this pronunciation was more desirable due to its perceived modernity.
Were the Wissenschaft folks even aware of the Yemenite pronunciation?
Not until Even Sapir by Rabbi Yaakov Sapir was published in the 1860s.
As far as whether they considered Sefaradit most pure, it's not monolithic. Shadal, for example, believed that the Ashkenazic qomatz followed the Tiberian masorah. He also pointed out that in Syriac there are two pronunciations, one which has a qomatz pronounced like the Ashkenazim, /o/, and the other which pronounces those vowels as /ah/ which is similar to the Sephardim. Thus, to the extent that we are obliged to follow the Tiberian masorah, the Ashkenazim were correct here. But to the extent that language develops naturally, both are correct and have an internal logic.
To a certain degree the issue was not which was more correct, but which was more aesthetically pleasing. It was more immediately obvious that the European pronunciations were European and thus, in their view, corrupted. It was difficult for a Galician maskil, for example, to see his native pronunciation as equally correct and equally pleasant as Sefaradit. Furthermore, the Sefaradit was accepted academic convention, so it made sense to conform with it, at least in writings which were meant to be academic.
Maybe just because a true Yemenite pronunciation would be pretty difficult for most Ashkenazic Jews? It uses several phonemes that are common in Arabic, but rare in the European languages. (I seem to remember a similar reason for why Israeli Hebrew, while officially Sephardic in pronunciation, in practice uses the least common denominator among the Ashkenazic and Sephardic consonantal values.)
This is not consistent. A couple weeks ago I went to a Conservative congregation for kabbalat shabbat and it was Ashkenazi all the way. On the other hand, another Conservative shul I'm familiar with is mostly led in Israeli pronunciation. On the third hand, many individuals in that congregation, when called for aliyot, use Ashkenazi.
I think this answer is correct with respect to what's being taught in the schools. In terms of what you hear in shul otherwise, it's a mix and will presumably be so until most attendees are products of the current curriculum (or imports from other Israeli-Hebrew traditions).
Why should Wissenschaft lead them to the Yemenite pronunciaton?
Isn't Wissenschaft about finding the "most authentic" ancient pronunciation. Wouldn't the presence of the Jimmel (an affricate) make that claim to authenticity suspect when a Ghimmel (a fricative) seems to better fit a consistent pattern for בגד כפת, namely that these letters should all be fricatives when the dagesh is absent, and stops when the dagesh is present?
First I take “wissenschafft” to mean logic, rationality, or science. The foregoing would seem to point to the pronunciation that is most authentic in light of the original pronunciation, to the extent that it can be inferred from Linguistics and giving some regard to the Masoretic vowel system, even though they were writing about 600 years after the cessation of Hebrew as a vernacular. The Conservative movement simply followed Israel’s lead where the decision of the Hebrew Language Committee (Va'ad Halashon)was to adopt Sephardic but against which European “ ‘olim” balked when it came to consonants which they had difficulty pronouncing, such as the gutturals and the fricative alternates of gimel, tav, and dalet. Thus we ended up with what we have today: a purely Semitic grammar coupled with a Europeanized consonant system.