The fact the German quota was not filled during the 1930s did not affect German Jews - Jews were separately described for quotas ("Hebrews"). The reality is the majority of the Jews who died in the Holocaust were those who were unable to emigrate as they were in countries occupied by Germany after the war started. Only a small number of Jews from occupied countries were able to leave where they were and get to someplace where they could, even theoretically, get to someplace the Germans were not going to occupy.
It is difficult to get a handle on how many Jews from countries that had some level of increasing antisemitic policies/history in the 1930s tried to emigrate to one of these countries outside of continental Europe (including Palestine). Hungary, Baltic States, Romania, Italy, and Poland would be some of these. None of these listed "safe" countries would be very welcoming for immigrants from the USSR except under special circumstances. To the extent the Jews of those countries would be willing to emigrate between 1933 and 1939, that would represent those who could be saved from occupied countries. Very few Jews in France, Holland, Belgium, Denmark, Norway were looking to emigrate before WWII so changing quotas would have little effect on those unfortunates.
If you push the POD back to the 1920s, then of course not having Jews as a separate category would make a big difference for the USA. Likewise the UK opening up Palestine would make a big difference. Sadly, IMHO, both of those would require intervention of Skippy the ASB.