You dont even address those religious Gedolim who call themselves zionists(with no relation to secular zionism)i.e Hacham Mordechai Eliyahu or those who permit hallel without a baracha i.e Rav Ovadiah Yosef.
But the historian Tzvi Weinman later showed Kasher's claims to be a falsification of the facts. In an article published in Digleinu (Shvat 5739) during Kasher's lifetime, and later in his book Mikatowitz Ad Hei B'Iyar (pp. 134-136), Weinman showed that the original declaration read not "beginning of redemption" but "beginning of the ingathering of the exiles". Furthermore, the declaration was sent to the rabbis to sign, together with a notice that if the rabbi did not reply in the negative, his silence would be taken as consent to the declaration. (This explains why the signature of Rabbi Menachem Kuperstock appears despite that fact that he passed away 2 years earlier.) Furthermore, the declaration was sent in three different versions to different rabbis, and many of the rabbis signed on versions that did not include any positive words about the state, just about voting for the United Front. The 1949 activists who posted the announcement in the streets took all the signatures and put them under one declaration. Furthermore, there were actually two other announcement published at the time of that election, one signed by roshei yeshivos and one signed by Chassidic rebbes. Kasher took all the names of the signatories on all three announcements and claimed that they had all signed the one calling the state "the beginning of redemption".
Other than this evidence from Kasher's book, Rabbi Yosef, quite uncharacteristically for someone with his breadth of knowledge, does not give any Talmudic arguments or proofs to explain why it is permitted in his opinion to found a state.