If the MT is acknowledged to not be the original Hebrew then why is it given precedence over the Septuagint (it seems) by scholars?
Because it isn't the original Hebrew either, seeing as how it isn't Hebrew at all.
Or maybe not. I'm not a translator myself, but as I understand it, the root issue is that all
the OT sources have significant problems. The MT is obviously damaged; the LXX has obvious mistranslations; the DSS are fragmentary. It is in fact clear that to some degree, the LXX does represent an earlier version of the text than the MT, because the DSS agrees with the former against the latter. But some of the time, it seems to be just wrong.
And remember, the problem in this specific case isn't the text, really, but rather, how the text is translated. The LXX is important as a testimony to that translation, whereas the MT doesn't testify at all, because it (most likely) is
the text. The contrary side here is provided by modern Jews, not by the Hebrew text. It's a much more straightforward argument that they are incorrect, especially if it can be shown that there are problems with applying this interpretation in other places in the text, than to postulate an ancient Hebrew text which does not survive.
As to why recent "liberal" translations prefer "young woman", it's because they are swayed by German theological precepts that are hostile to the miraculous in general and to the incarnation in particular.
Obviously it is impossible to effectively argue against a dogmatic faith in an inerrant version, since that faith must cover over any apparent defects in that text. But as an argument to others, such a precept is counterproductive.