Thanks for the direction to 'My Promised Land' - will look it up.
Re actions to ensure Jews moved to Palestine rather than elsewhere, a couple of sources here.
Harry Howard of US State Department (and US delegate to UN) stated: "... there was discussion of liberalizing American immigration laws in this period. The Zionists opposed that liberalization on the ground that this would not be a solution as far as they were concerned. They wanted a political, not necessarily a humanitarian, solution --that is, they wanted a state. Mr. Truman himself has testified in his Memoirs that he was never under such pressure on any other problem. In this problem he was under terrific pressure." (para 68, trumanlibrary.org/oralhist/howardhn#transcript).
According to Baruch Kimmerling: "Grodzinsky tells us with great pain how Ben-Gurion and other Zionist leaders vetoed the immigration of 1,000 orphans, who were in physical and emotional danger as a result of the harsh winter of 1945, from the camps in Germany to England, where the Jewish community had managed to secure them permits. Another group of roughly 500 children of camp inhabitants was barred, after Zionist intervention, from reaching France, whose rabbinical institutions had offered them safe haven." (www.thenation.com/article/israels-culture-martyrdom?page=full#)
Kimmerling also states: " Zertal makes clear in an illuminating discussion of the odyssey of the 4,500 survivors from German camps who set sail in July 1947 as "illegal immigrants" on a ship later named Exodus. The real story of the ship was far less glorious than the one told in Leon Uris's 1958 bestseller and Otto Preminger's 1960 film. When the ship embarked, the UN Special Committee on Palestine was holding discussions and Ben-Gurion, the head of the Jewish Agency, the primary governing body of the state-in-formation, felt that the plight of Jewish refugees in Europe needed to be dramatized in order to attract more sympathy for the Jewish struggle over Palestine. The British authorities had refused to let the immigrants disembark in Palestine, or even to take refuge in transitional camps in Cyprus, forcing the boat to be redirected back to Germany. To prevent such a ghastly outcome, Zionist leader Chaim Weizmann persuaded the French Prime Minister, Leon Blum, to host the refugees. Ben-Gurion rejected this solution out of hand, and the poor survivors remained on board for seven months."
And from Alison Weir's organisation: “The Zionist movement...interfered with and hindered other organizations, Jewish and non-Jewish, whenever it imagined that their activity, political or humanitarian, was at variance with Zionist aims or in competition with them, even when these might be helpful to Jews, even when it was a question of life and death...Beit Zvi documents the Zionist leadership’s indifference to saving Jews from the Nazi menace except in cases in which the Jews could be brought to Palestine...[e.g.] the readiness of the dictator of the Dominican Republic, Rafael Trujillo, to absorb one hundred thousand refugees and the sabotaging of this idea — as well as others, like proposals to settle the Jews inAlaska and the Philippines — by the Zionist movement... (ifamericansknew.org/history/origin.html).