Hi Chaim,
I understand your position insofar as not willing to give a support to Bibi for the dubious benefit of increasing your chances of moving to Israel. That is understandable.
But here is a major flaw with your logic: you suggested that you are not ready to sacrifice your principles and interests of Jewish people to gain personal benefits and, even, for larger benefits to JTF. I don't see this dichotomy. I don't see how your interests and interests of JTF, as a whole, are separable from the interests of the Jewish nation. In fact, you being in Galut is of extreme detriment to Jewish people. Much more so than your personal perception of "integrity". You open support for Likud may not be able to increase your chances of getting in, but it will increase them. At a card table, you can't play goody-goody with cheaters. I think you need to talk to people in Likud, Israel Beitenu, National Unity to explore inroads for securing "favorable" review of your application.
And, G-d forbid to see the day when Jewish people will appeal to "honest" Chaim to come from exile to save them. You know, that this will happen, if it will, only after a national tragedy. And we can't afford that. I am not asking you to trade yours and our principles - I am asking you to be more pragmatic, to assign priorities to our objectives. The highest one, IMO, is for you to make Alia - your appeal is mostly for Israelis, I doubt that we can build it big in America, but there is no doubt in my mind that you (we) can make it big in Israel.
Shalom and good luck!