The 2nd linked study controlled for intended major and still showed prediction of graduation rate was nearly identical with and without SAT score. That said, there is a correlation between SAT score and major. The degree of this correlation varies tremendously among individual colleges, depending on things like whether they admit by major/school or not, and generally if they have different admissions expectations and emphases for different majors.
The Duke study at http://public.econ.duke.edu/~psarcidi/grades_4.0.pdf looked into what sections of the major influenced switch out out of an engineering, natural sciences, economics major with attempting to control for individual courses as you described, by looking at the grade distribution of specific courses. With all controls, it found that all sections of the application they considered had some degree of correlation with switching out except for “personal qualities” . This includes things like the ratings admissions officers gave to LORs and essays. With all controls, they found that by far the most influential components of the application in this switching behavior were gender and admissions rating of HS curriculum, rather than scores. It is also important to note that even with all controls, all of these studies could only explain a minority of variation in measures of academic success in college. For example, I mentioned the UC study model could explain ~26% of variation in GPA with all controls. The bulk of the variation in academic success during college seems to depend on other things besides the metrics used in studies.