What are the rules for the pronunciation of phonemic stress (milel and milra) in the Aramaic of the Bavli, and how do they differ from Hebrew and/or the Aramaic of the Targums (if at all)? None of the grammar books I've read address this question head on; anyone know of a source that does?
I would take an example from the book of Daniel, which has a lot of Aramaic. Luckily Keter Aram Tzova exists for this book (and the people of Aram Tzova spoke Aramaic). And Keter Aram Tzova has the "stresses" (milel/milra) annotated. See, for example, Daniel perek gimel (chapter 3)
Under these assumptions, milra wins :)
In his seminal book Introduction to the Grammar of Jewish-Babylonian Aramaic, E. Bar Asher Segal writes that it "is almost impossible to reconstruct [...] the position of the stress."
He cites S. Morag's Babylonian Aramaic: The Yemenite Tradition (1988: 117-119) who "argues that it is difficult to propose consistent rules even within the Yemenite tradition", a tradition with the highest historical fidelity among all living Aramaic reading traditions.
Having studied a bit with a native Aramaic speaker (Kurdish/Assyrian Jew) and from having Aramean Christians marry intermarry into my family I have come to the following conclusion. Aramaic is similar to Hebrew when it comes to emphasis. Which means most words should have emphasis on the final syllable. However, like Arabic it has more exceptions for earlier emphasis, but still nowhere near as much as is done by Ashkenazim.
I don't think there is a written Masorah for the Bavli's pronunciation. However, I live in Detroit suburbs where there are a lot of native neo-Aramaic speakers and they generally pronounce the language mille'el i.e., penultimate stress. This is obviously not like Biblical Aramaic, which is mille'ra. For example, one guy told me that "I hate" would be pronounced qsaNIne.