While the kids immigrants who came as PhD students and skilled workers in math-heavy areas (e.g. engineering and computing) skew today’s Asian SAT score averages upward and even more so the math section score averages (while having a much smaller effect on other racial and ethnic groups due to relative numbers of those immigrants versus the pre-existing or other immigrant populations in the other racial and ethnic groups), there does not seem to be that much of a current skew toward the EBRW section compared to the math section overall (<20 points in favor of the EBRW in every other racial/ethnic group, according to Fast Facts: SAT scores (171) , versus the much larger differences in the converted 1960 scores).
Note that some of the colleges in the table above (Amherst, Columbia, Princeton, Yale) were male-only in 1960, but they still exhibited a section skew in favor of the verbal-converted-to-EBRW score over the math score despite the current tendency of male SAT takers to do (slightly) better on the math section.