I agree that there is cognative dissonance on the part of the Jews. Their reaction began way before Roosevelt, before the turn of the century. It is hard to conceive, now, how ferocious, scary, all-pervasive and overt anti-Semitism was then. The Dems pretended to be slightly welcoming, whereas the Republicans didn’t bother. The mass of Jewish immigrants at the end of the 19th century were impoverished working class people. They still identify with that scenario.
I would disagree with your chronology. I would say that 1928 was really the first presidential election in which the later arriving Eastern European Jewish immigrants and their descendants predominated among Jewish voters and swung the Jewish vote strongly to the 'Rats. (BTW, you might be surprised to know that the Herbert Hoover campaign for re-election in 1932 did engage in specifically soliciting Jewish voters; the RNC published at least one pamphlet in Yiddish with Hoover's photo on it extolling the merits of the candidate for Yiddish language readers.)
For the previous half-century or more, the Jewish electorate was composed percentagewise more of earlier German Jewish immigrants and their descendants who were generally much wealthier (some were famous entrepreneurs) and more assimilated and tended to be Republicans with an affinity for the legacy of Lincoln. The best reference on these German Jewish immigrants and their descendants in the late 19th century is the book "Our Crowd," by Stephen Birmingham, which was a best-seller when it was released c. 1970(?).