@philospher
It’s more than likely due to vowel shifts (which do occur – English went through a major one in the 1400-1700s; Yiddish did something similar but collapsed vowels into each other) and the effect of Umlaut (I can’t link the Wikipedia article here per forum rules), and the simple fact that Yiddish’s Hebrew component is large enough and used on a daily basis for those changes to be able leak straight into davening, leining, etc. (the Halachik issues are irrelevant to this discussion, but they most certainly exist.)
As for Chassidim worldwide using Hebrew heavily influenced by Hungarian/Southeastern/Transcarpathian Yiddish, I believe that is due to cultural factors, specifically the Holocaust, which drove the various branches of Chassidim together and everyone more or less adopted the Satmar/Vitzhnitz pronunciation because they were dominant.
In terms of the linguistics, you’re talking about an isogloss (a linguistic border that delineates between dialects, languages or specific features). I don’t have an accurate map (Google doesn’t have one either), but there is one that runs roughly through southern Poland, Hungary and into Ukraine, which would partially explain it.
I will point out that Chabad – which is technically a Chassidish branch (let’s please not get into a discussion of that) has for the most part maintained its Northeastern Yiddish flavor (saying “tejrah” rather than “toirah” or ever “torah”) outside of Israel (Israel is a different story, like it is with all things).
I can look into it more, but I don’t live near an academic library (I live in northern Israel and the relevant academic library is in Ramat Gan).