Actually, Toi, the Vilna Gaon’s entire discussion of the idea, of Moshiach (both ben Yosef and ben David – which were you talking about?) is found in the sefer Kol HaTor, which he wrote with his Great-Nephew Rav Hillel Shklover. In it, he introduces his formula for the “yomim” that will pass from the time he determined began the atchalta degeula (5500 or 1740 CE) until the zman. The nearest that it comes to the dates you cite in your post (I don’t know if you are talking about November 1947 at the UN, or May 1948) is two to three years earlier in 1945. He was pretty clear about the dates in his sefer. Check it out, its in the first perek.
BTW, there is a huge amount of evidence and information in his sefer that provides support for the establishment of a state, for example, his interpretation that it can be taken by force if necessary.